<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-05-08</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001578845</issuerCik>
        <issuerName>Allergan plc</issuerName>
        <issuerTradingSymbol>AGN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001712446</rptOwnerCik>
            <rptOwnerName>Boccuzi Joseph H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CLONSHAUGH BUSINESS AND</rptOwnerStreet1>
            <rptOwnerStreet2>TECHNOLOGY PARK, COOLOCK, CO.</rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>D17 E400</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $0.0001</value>
            </securityTitle>
            <transactionDate>
                <value>2020-05-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3605</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects the disposition of ordinary shares (&quot;Allergan Shares&quot;) of Allergan plc (&quot;Allergan&quot;) as contemplated by the Transaction Agreement dated as of June 25, 2019 among AbbVie Inc. (&quot;AbbVie&quot;), Venice Subsidiary, LLC (&quot;Acquirer Sub&quot;) and Allergan (the &quot;Transaction Agreement&quot;), pursuant to which Acquirer Sub acquired Allergan pursuant to a scheme of arrangement under Chapter 1 of Part 9 of the Irish Companies Act of 2014 and the capital reduction under Sections 84 and 85 of the Act (the &quot;Scheme&quot;).  In accordance with the terms of the Transaction Agreement, at the effective time of the Scheme, each Allergan Share was converted into $120.30 in cash and 0.8660 of a newly issued share of AbbVie common stock, par value $0.01 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kira M. Schwartz, Attorney-in-Fact for the Reporting Person</signatureName>
        <signatureDate>2020-05-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
