Exhibit 5.1

FACSIMILE DIRECT DIAL NUMBER

June 4, 2021

Northern Star Investment Corp. II

c/o Graubard Miller

The Chrysler Building

405 Lexington Avenue

New York, NY 10174

Dear Sirs:

Re: Registration Statement on Form S-4 (File No. 333-255120)

Ladies and Gentlemen:

We have acted as counsel to Northern Star Investment Corp. II, a Delaware corporation (the “Company”), in connection with the transactions contemplated by the Agreement and Plan of Reorganization, dated as of February 21, 2021 (“Merger Agreement”), by and among the Company, NSIC II-A Merger LLC, a Delaware limited liability company and wholly-owned subsidiary of the Company (“Merger Sub I”), NSIC II-B Merger LLC, a Delaware limited liability company and wholly-owned subsidiary of the Company (“Merger Sub II”), Apex Fintech Solutions LLC (f/k/a Apex Clearing Holdings LLC), a Delaware limited liability company (“Apex Fintech”) and, solely for the purposes of Section 5.21 therein, PEAK6 Investments LLC, a Delaware limited liability company (“PEAK6”).

Pursuant to the Merger Agreement, (i) Merger Sub I will merge with and into Apex Fintech (the “Initial Merger”), with Apex Fintech being the surviving entity (the “Initial Surviving Company”) of the Initial Merger and Apex Fintech’s members receiving shares of Class A common stock, par value $0.0001 per share, of Northern Star (which shall be redesignated as common stock, without class designation, in connection with the transactions contemplated by the Merger Agreement, the “Common Stock”) in exchange for their membership interests in Apex Fintech, and (ii) immediately following the Initial Merger and as part of the same overall transaction as the Initial Merger, the Initial Surviving Company will merge with and into Merger Sub II (the “Final Merger” and, together with the Initial Merger, the “Mergers”), with Merger Sub II being the surviving entity of the Final Merger (the “Final Surviving Company”). As a result of the Mergers, Apex Fintech will become a wholly owned subsidiary of the Company, with the members of Apex Fintech becoming stockholders of Northern Star.

This opinion is being rendered at the request of the Company in connection with the registration by the Company under the above-referenced Registration Statement (together with all amendments thereto as of the date hereof, the “Registration Statement”) filed with the United States Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), of up to 470,000,000 shares of Common Stock.

Northern Star Investment Corp. II

June 4, 2021

Page 2 of 2

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinions hereinafter set forth below. These documents included, without limitation, (i) the Registration Statement, and all amendments thereto filed with the Commission prior to the date hereof; (ii) the Merger Agreement; (iii) the Company’s Second Amended and Restated Certificate of Incorporation, and (iv) the resolutions adopted by the board of directors of the Company relating to the Registration Statement and the Merger Agreement. With respect to such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as reproduced or certified copies, and the authenticity of the originals of those latter documents. As to all questions of fact material to these opinions, we have, to the extent deemed appropriate, relied upon certain representations of certain officers and employees of the Company.

In connection with the opinions expressed below, we have assumed that, at and prior to the time of the issuance and delivery of any securities by the Company pursuant to the Registration Statement, (i) the Registration Statement will have been declared effective and no stop order suspending the effectiveness of the Registration Statement has been issued and no proceedings with respect thereto have been commenced or threatened, (ii) the transactions contemplated by the Merger Agreement and the Registration Statement will have been consummated in accordance with the terms of the documents pertaining thereto, without any waiver or breach of any material terms or provisions thereof, and that such transactions will be effective under applicable law, and (iii) the shareholders of the Company will have approved the Merger Agreement and the other proposals set forth in the proxy statement/prospectus included in the Registration Statement, including the proposals to approve the Second Amended and Restated Certificate of Incorporation, which are to be presented and voted upon at the meeting as set forth in the proxy statement/prospectus included in the Registration Statement.

Based on the foregoing, and subject to the qualifications stated herein, we are of the opinion that the Common Stock, when issued in the manner and on the terms described in the Registration Statement and the Merger Agreement, will be validly issued, fully paid and non-assessable.

The opinions expressed herein are limited to the laws of the State of New York and the corporate laws of the State of Delaware, and we express no opinion as to the effect on the matters covered by this letter of the laws of any other jurisdiction. The opinions expressed herein are rendered as of the date hereof and are based on existing law, which is subject to change. Where our opinions expressed herein refer to events to occur at a future date, we have assumed that there will have been no changes in the relevant law or facts between the date hereof and such future date. We do not undertake to advise you of any changes in the opinions expressed herein from matters that may hereafter arise or be brought to our attention or to revise or supplement such opinions should the present laws of any jurisdiction be changed by legislative action, judicial decision or otherwise.

Our opinions expressed herein are limited to the matters expressly stated herein and no opinion is implied or may be inferred beyond the matters expressly stated.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement, to the use of our name as your counsel and to all references made to us in the Registration Statement and in the proxy statement/prospectus forming a part thereof. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act, or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Graubard Miller