Exhibit 5.1

Our ref MUL/683401-000001/60444228v3

Theravance Biopharma, Inc.

PO Box 309, Ugland House

Grand Cayman

KY1-1104

Cayman Islands

3 December 2019

Theravance Biopharma, Inc.

We have acted as counsel as to Cayman Islands law to Theravance Biopharma, Inc. (the “Company”) to provide this opinion letter in connection with the Company’s registration statement on Form S-3, including all amendments or supplements thereto, filed with the United States Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933 as amended (the “Act”) (including its exhibits, the “Registration Statement”) related to securities to be issued and sold by the Company from time to time (together, the “Securities”). The Securities include:

(a)ordinary shares of the Company of a par value of US$0.0001 each (“Shelf Shares”);

(b)warrants to purchase Shelf Shares or Debt Securities (as defined below) (“Warrants”) issuable pursuant to the terms of a warrant agreement (the “Warrant Agreement”) and warrant certificate (the “Warrant Certificate” and, together with the Warrant Agreement, the “Warrant Documents”);

(c)debt securities, including senior debt securities, senior subordinated debt securities, subordinated debt securities, convertible debt securities and exchangeable debt securities of the Company (the “Debt Securities”), each series of Debt Securities to be issued under an indenture to be entered into by the Company and the trustee, substantially in the form attached as an Exhibit to the Registration Statement, as each such indenture may be supplemented, in connection with the issuance of each such series, by a supplemental indenture, officers’ certificate or other writing thereunder establishing the form and terms of such series;

(d)purchase contracts, including contracts obligating holders to purchase from or sell to the Company, and obligating the Company to sell to or purchase from the holders, Shelf Shares (“Purchase Contracts”), such Purchase Contracts to be issued separately or as part of purchase units (“Purchase Units”) which may be comprised of one or more Purchase Contracts and

beneficial interests in Debt Securities, debt obligations of third parties, including U.S. treasury securities or any other securities described above;

(e)ordinary shares of the Company of a par value of US$0.0001 each (“Sales Agreement Shares” and, together with the Shelf Shares, “Ordinary Shares”) to be issued pursuant to the terms of a sales agreement (the “Sales Agreement”) between the Company and Cowen and Company, LLC;

This opinion letter is given in accordance with the terms of the Legal Matters section of the Registration Statement.

1Documents Reviewed

We have reviewed originals, copies, drafts or conformed copies of the following documents:

1.1The certificate of incorporation dated 29 July 2013 and the amended and restated memorandum and articles of association of the Company as registered or adopted on 28 April 2014 (the “Memorandum and Articles”).

1.2The certificate in respect of the minutes (the “Minutes”) of the meeting of the board of directors of the Company held on 24 October 2019 (the “Meeting”) and the corporate records of the Company maintained at its registered office in the Cayman Islands.

1.3A certificate of good standing with respect to the Company issued by the Registrar of Companies (the “Certificate of Good Standing”).

1.4A certificate from a director of the Company a copy of which is attached to this opinion letter (the “Director’s Certificate”).

1.5The Registration Statement.

1.6The form of the Sales Agreement.

1.7The form of indenture in respect of the Debt Securities (the “Indenture” and, together with the Warrant Documents, the Purchase Contracts, the Purchase Units and the Sales Agreement, the “Documents”).

2Assumptions

The following opinions are given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion letter. These opinions only relate to the laws of the Cayman Islands which are in force on the date of this opinion letter. In giving the following opinions, we have relied (without further verification) upon the completeness and accuracy, as at the date of this opinion letter, of the Director’s Certificate and the Certificate of Good Standing. We have also relied upon the following assumptions, which we have not independently verified:

2.1The Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture have been, or will be, authorised and duly executed and unconditionally delivered by or on behalf of all relevant parties in accordance with all relevant laws.

2.2The Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture are, or will be, legal, valid, binding and enforceable against all

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relevant parties in accordance with their terms under the laws of the State of New York (the “Relevant Law”) and all other relevant laws (other than, with respect to the Company, the laws of the Cayman Islands).

2.3The choice of the Relevant Law as the governing law of the Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture has been made in good faith and would be regarded as a valid and binding selection which will be upheld by the courts of the State of New York and any other relevant jurisdiction (other than the Cayman Islands) as a matter of the Relevant Law and all other relevant laws (other than the laws of the Cayman Islands).

2.4Copies of documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals.

2.5All signatures, initials and seals are genuine.

2.6The capacity, power, authority and legal right of all parties under all relevant laws and regulations (other than, with respect to the Company, the laws of the Cayman Islands) to enter into, execute, unconditionally deliver and perform their respective obligations under the Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture.

2.7There is no contractual or other prohibition or restriction (other than as arising under Cayman Islands law) binding on the Company prohibiting or restricting it from entering into and performing its obligations under the Documents.

2.8No monies paid to or for the account of any party under the Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture or any property received or disposed of by any party to the Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture in each case in connection with the Documents, the Warrants issuable under the Warrant Documents and the Debt Securities issuable under the Indenture or the consummation of the transactions contemplated thereby represent or will represent proceeds of criminal conduct or criminal property or terrorist property (as defined in the Proceeds of Crime Law (2019 Revision) and the Terrorism Law (2018 Revision), respectively).

2.9The Debt Securities will be issued and authenticated in accordance with the provisions of a duly authorised, executed and delivered Indenture Document.

2.10The Indenture, the Warrants and the Warrant Documents, the Purchase Contracts and the Purchase Units will be, or have been, duly executed and delivered by an authorised person of the parties thereto.

2.11The Company will receive money or money’s worth in consideration for the issue of the Ordinary Shares and none of the Ordinary Shares will be issued for less than their par value.

2.12There will be sufficient Ordinary Shares authorised for issue under the Memorandum and Articles.

2.13The issue of the Warrants issuable under the Warrant Documents, the Purchase Contracts, the Purchase Units, the Debt Securities issuable under the Indenture and the Ordinary Shares will be of commercial benefit to the Company.

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2.14No invitation has been or will be made by or on behalf of the Company to the public in the Cayman Islands to subscribe for any of the Securities.

2.15There is nothing under any law (other than the laws of the Cayman Islands) which would or might affect the opinions set out below. Specifically, we have made no independent investigation of the Relevant Law.

Save as aforesaid we have not been instructed to undertake and have not undertaken any further enquiry or due diligence in relation to the transaction the subject of this opinion letter.

3Opinions

Based upon, and subject to, the foregoing assumptions and the qualifications set out below, and having regard to such legal considerations as we deem relevant, we are of the opinion that:

3.1The Company has been duly incorporated as an exempted company with limited liability and is validly existing and in good standing with the Registrar of Companies under the laws of the Cayman Islands.

3.2The Company has all requisite power and authority under the Memorandum and Articles to enter into, execute and perform its obligations under the Indenture to which it will be a party and the Debt Securities issuable under the Indenture to which it is, or will be, a party.

3.3With respect to each issue of Debt Securities pursuant to the Indenture, when: (a) the board of directors of the Company have taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; and (b) such Debt Securities issued thereunder have been duly executed and delivered on behalf of the Company and authenticated in the manner set forth in the Indenture relating to such issue of Debt Securities and delivered against due payment therefor pursuant to, and in accordance with, the terms of the Registration Statement and any relevant prospectus supplement, such Debt Securities issued pursuant to the Indenture will have been duly executed, issued and delivered.

3.4With respect to the Ordinary Shares, when: (a) the board of directors of the Company has taken all necessary corporate action to approve the issue thereof, the terms of the offering thereof and related matters; (b) the issue of such Ordinary Shares has been recorded in the Company’s register of members (shareholders); and (c) the subscription price of such Ordinary Shares (being not less than the par value of the Ordinary Shares) has been fully paid in cash or other consideration approved by the board of directors of the Company, the Ordinary Shares will be duly authorised, validly issued, fully paid and non-assessable.

3.5With respect to the Purchase Contracts and the Purchase Units, when: (a) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Purchase Contracts and the Purchase Units and to approve the issue thereof, the terms of the offering thereof and related matters; (b) a Purchase Contract or Purchase Unit shall have been duly authorised and validly executed and delivered by the Company; and (c) the Purchase Contracts and the Purchase Units have been duly executed, countersigned, registered and delivered in accordance with the applicable Purchase Contract or Purchase Unit and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Purchase Contracts and the Purchase Units will be duly authorised, legal and binding obligations of the Company.

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3.6With respect to the Warrants, when: (a) the board of directors of the Company has taken all necessary corporate action to approve the creation and terms of the Warrants and to approve the issue thereof, the terms of the offering thereof and related matters; (b) a Warrant Agreement relating to the Warrants shall have been duly authorised and validly executed and delivered by the Company and the financial institution designated as warrant agent thereunder; and (c) the Warrant Certificates have been duly executed, countersigned, registered and delivered in accordance with the Warrant Agreement relating to the Warrants and the applicable definitive purchase, underwriting or similar agreement approved by the board of directors of the Company upon payment of the consideration therefor provided therein, the Warrants will be duly authorised, legal and binding obligations of the Company.

4Qualifications

The opinions expressed above are subject to the following qualifications:

4.1The obligations assumed by the Company under the Documents or the relevant Securities issuable thereunder will not necessarily be enforceable in all circumstances in accordance with their terms. In particular:

(a)enforcement may be limited by bankruptcy, insolvency, liquidation, reorganisation, readjustment of debts or moratorium or other laws of general application relating to or affecting the rights of creditors;

(b)enforcement may be limited by general principles of equity. For example, equitable remedies such as specific performance may not be available, inter alia, where damages are considered to be an adequate remedy;

(c)some claims may become barred under relevant statutes of limitation or may be or become subject to defences of set off, counterclaim, estoppel and similar defences;

(d)where obligations are to be performed in a jurisdiction outside the Cayman Islands, they may not be enforceable in the Cayman Islands to the extent that performance would be illegal under the laws of that jurisdiction;

(e)the courts of the Cayman Islands have jurisdiction to give judgment in the currency of the relevant obligation and statutory rates of interest payable upon judgments will vary according to the currency of the judgment. If the Company becomes insolvent and is made subject to a liquidation proceeding, the courts of the Cayman Islands will require all debts to be proved in a common currency, which is likely to be the “functional currency” of the Company determined in accordance with applicable accounting principles. Currency indemnity provisions have not been tested, so far as we are aware, in the courts of the Cayman Islands;

(f)arrangements that constitute penalties will not be enforceable;

(g)enforcement may be prevented by reason of fraud, coercion, duress, undue influence, misrepresentation, public policy or mistake or limited by the doctrine of frustration of contracts;

(h)provisions imposing confidentiality obligations may be overridden by compulsion of applicable law or the requirements of legal and/or regulatory process;

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(i)the courts of the Cayman Islands may decline to exercise jurisdiction in relation to substantive proceedings brought under or in relation to the Documents in matters where they determine that such proceedings may be tried in a more appropriate forum;

(j)any provision in a Document which is governed by Cayman Islands law purporting to impose obligations on a person who is not a party to such Document (a “third party”) is unenforceable against that third party. Any provision in a Document which is governed by Cayman Islands law purporting to grant rights to a third party is unenforceable by that third party, except to the extent that such Document expressly provides that the third party may, in its own right, enforce such rights (subject to and in accordance with the Contracts (Rights of Third Parties) Law, 2014 of the Cayman Islands);

(k)any provision of a Document which is governed by Cayman Islands law which expresses any matter to be determined by future agreement may be void or unenforceable;

(l)we reserve our opinion as to the enforceability of the relevant provisions of the Documents to the extent that they purport to grant exclusive jurisdiction as there may be circumstances in which the courts of the Cayman Islands would accept jurisdiction notwithstanding such provisions; and

(m)a company cannot, by agreement or in its articles of association, restrict the exercise of a statutory power and there is doubt as to the enforceability of any provision in the Documents whereby the Company covenants to restrict the exercise of powers specifically given to it under the Companies Law (2018 Revision) (the “Companies Law”), including, without limitation, the power to increase its authorised share capital, amend its memorandum and articles of association or present a petition to a Cayman Islands court for an order to wind up the Company;

(n)if the Company becomes subject to Part XVIIA of the Companies Law, enforcement or performance of any provision in the Documents which relates, directly or indirectly, to an interest in the Company constituting shares, voting rights or director appointment rights in the Company may be prohibited or restricted if any such relevant interest is or becomes subject to a restrictions notice issued under the Companies Law; and

(o)enforcement or performance of any provision in the Documents which relates, directly or indirectly, to an interest in a Cayman Islands company or limited liability company constituting shares, membership interests, voting rights or director or manager appointment rights in respect of such company or limited liability company may be prohibited or restricted if any such relevant interest is or becomes subject to a restrictions notice issued under the Companies Law or the Limited Liability Companies Law (2018 Revision).

4.2To maintain the Company in good standing with the Registrar of Companies under the laws of the Cayman Islands, annual filing fees must be paid and returns made to the Registrar of Companies within the time frame prescribed by law.

4.3We express no opinion as to the meaning, validity or effect of any references to foreign (i.e. non-Cayman Islands) statutes, rules, regulations, codes, judicial authority or any other promulgations and any references to them in the Documents or the relevant Securities issuable thereunder.

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4.4We have not reviewed the final forms of the Indenture, the Debt Securities to be issued thereunder, the Warrant Documents or the Warrants to be issued thereunder, the Purchase Contracts or the Purchase Units, and our opinions are qualified accordingly.

4.5We reserve our opinion as to the extent to which the courts of the Cayman Islands would, in the event of any relevant illegality or invalidity, sever the relevant provisions of the Indenture, the Debt Securities, the Warrant Documents, the Warrants, the Purchase Contracts or the Purchase Units and enforce the remainder of the Indenture, the Debt Securities, the Warrant Documents, the Warrants, the Purchase Contracts or the Purchase Units or the transaction of which such provisions form a part, notwithstanding any express provisions in the Indenture in this regard.

4.6Under Cayman Islands law, the register of members (shareholders) is prima facie evidence of title to shares and this register would not record a third party interest in such shares. However, there are certain limited circumstances where an application may be made to a Cayman Islands court for a determination on whether the register of members reflects the correct legal position. Further, the Cayman Islands court has the power to order that the register of members maintained by a company should be rectified where it considers that the register of members does not reflect the correct legal position. As far as we are aware, such applications are rarely made in the Cayman Islands and there are no circumstances or matters of fact known to us on the date of this opinion letter which would properly form the basis for an application for an order for rectification of the register of members of the Company, but if such an application were made in respect of the Ordinary Shares, then the validity of such shares may be subject to re-examination by a Cayman Islands court.

We express no view as to the commercial terms of the Documents or the relevant Securities issuable thereunder or whether such terms represent the intentions of the parties and make no comment with regard to warranties or representations that may be made by the Company.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the reference to our firm under the heading “Legal Matters” in the prospectus included in the Registration Statement. In providing our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the Rules and Regulations of the Commission thereunder.

The opinions in this opinion letter are strictly limited to the matters contained in the opinions section above and do not extend to any other matters. We have not been asked to review and we therefore have not reviewed any of the ancillary documents relating to the Documents or the relevant Securities issuable thereunder and express no opinion or observation upon the terms of any such document.

Yours faithfully

/s/ Maples and Calder

Maples and Calder

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