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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2015-01-02</periodOfReport>

    <dateOfOriginalSubmission>2015-01-06</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000077360</issuerCik>
        <issuerName>PENTAIR plc</issuerName>
        <issuerTradingSymbol>PNR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001189049</rptOwnerCik>
            <rptOwnerName>HOGAN RANDALL J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5500 WAYZATA BLVD., SUITE 800</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GOLDEN VALLEY</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55416</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman &amp; Chief Exec. Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares - Restricted Stock Units</value>
            </securityTitle>
            <transactionDate>
                <value>2015-01-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>46991</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>295778</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2015-01-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3156</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>66.68</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55559</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2015-01-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>21336</value>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>63.96</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>83494</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock units granted pursuant to and subject to a vesting condition of the Pentair plc 2012 Stock and Incentive Plan.  Each restricted stock unit represents a right to receive one share of Pentair plc common shares upon vesting.</footnote>
        <footnote id="F2">End-of-period holdings reflect the vesting of restricted stock units that were previously reported.</footnote>
        <footnote id="F3">The Form 4 filed on January 6, 2015, reported that the reporting person held 294,553 shares following the reported transaction.  This amended Form 4 is being filed to report that the reporting person actually held 295,778 shares following the transaction.</footnote>
        <footnote id="F4">Shares surrendered to pay taxes applicable to vesting of restricted stock units.</footnote>
        <footnote id="F5">The Form 4 filed on January 6, 2015 reported 3,400 shares were surrendered to pay taxes applicable to the vesting of restricted stock units. This amended Form 4 is being filed to report that 3,156 shares were actually surrendered for the payment of this tax liability and to correct the number of shares beneficially owned following the reported transaction.</footnote>
        <footnote id="F6">The Form 4 filed on January 6, 2015 reported 19,209 shares were surrendered to pay taxes applicable to the vesting of restricted stock units. This amended Form 4 is being filed to report that 21,336 shares were actually surrendered for the payment of this tax liability and to correct the number of shares beneficially owned following the reported transaction.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John K. Wilson, Attorney-in-Fact for Randall J. Hogan</signatureName>
        <signatureDate>2015-01-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
