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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-08-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001802768</issuerCik>
        <issuerName>Royalty Pharma plc</issuerName>
        <issuerTradingSymbol>RPRX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001814899</rptOwnerCik>
            <rptOwnerName>Lloyd George W.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ROYALTY PHARMA PLC</rptOwnerStreet1>
            <rptOwnerStreet2>110 EAST 59TH STREET</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Investments &amp; CLO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>LP interests in RPI US Partners 2019, LP</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-08-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5555</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>55550</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>LP interests in RPI US Partners 2019, LP</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2502990</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>250299</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By GWL 2020 G, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>LP interests in RPI US Partners 2019, LP</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1726800</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>172680</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By GWL 2014 G, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>LP interests in RPI US Partners 2019, LP</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>81730</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8173</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By GWL 2013 NG, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">No limited partnership interests in RPI US Partners 2019, LP (&quot;RPI US LP&quot;) are being exchanged by the Reporting Person. Each limited partnership interest in RPI US LP (&quot;RPI US LP Interest&quot;) may be exchanged for ten Class B Interests in Royalty Pharma Holdings Limited (&quot;Holdings&quot;). Each Class B Interest in Holdings so distributed will be exchanged for one Class A Ordinary Share of the Issuer. Any exchanges will be made pursuant to the terms of the Exchange Agreement dated June 16, 2020, among the Issuer, Holdings, RPI US LP, RPI International Holdings 2019, LP, RPI International Partners 2019, LP and RPI EPA Holdings, LP (the &quot;Exchange Agreement&quot;). No additional value will be paid by the Reporting Person in connection with an exchange.</footnote>
        <footnote id="F2">The Reporting Person made a charitable donation of RPI US LP Interests. No Class A Ordinary Shares or RPI US LP Interests were sold.</footnote>
        <footnote id="F3">Represents RPI US LP Interests. Each RPI US LP Interest can be exchanged for ten Class B Interests in Holdings at any time and for no additional value, which exchange right does not expire until so converted. Upon such exchange, each Class B Interest in Holdings issued in exchange for a RPI US LP Interest will be exchanged for one Class A Ordinary Share of the Issuer for no additional value.</footnote>
    </footnotes>

    <remarks>In addition to the holdings disclosed above, the Reporting Person and family vehicles controlled by the Reporting Person hold 926,831 Class A Ordinary Shares and ICAI Interests exchangeable into 3,530,000 Class A Ordinary Shares.</remarks>

    <ownerSignature>
        <signatureName>/s/ Sean Weisberg, as Attorney-in-Fact for George W. Lloyd</signatureName>
        <signatureDate>2023-08-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
