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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-02-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096943</issuerCik>
        <issuerName>TELEFLEX INC</issuerName>
        <issuerTradingSymbol>TFX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001838834</rptOwnerCik>
            <rptOwnerName>Logue Daniel V.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>550 E. SWEDESFORD ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>WAYNE</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19087</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CVP, General Counsel &amp; Secty</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>171</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13303.888</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>300.876</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By 401(k) Trustee</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares consist of shares of common stock underlying performance stock units as to which the performance conditions were determined to be satisfied on February 24, 2025. These units are payable solely in shares of common stock, and remain subject to vesting on March 1, 2025.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Daniel V. Logue</signatureName>
        <signatureDate>2025-02-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0508
4
2025-02-24
0
0000096943
TELEFLEX INC
TFX
0001838834
Logue Daniel V.
550 E. SWEDESFORD ROAD
SUITE 400
WAYNE
PA
19087
0
1
0
0
CVP, General Counsel & Secty
0
Common Stock
2025-02-24
4
A
0
171
0
A
13303.888
D
Common Stock
300.876
I
By 401(k) Trustee
These shares consist of shares of common stock underlying performance stock units as to which the performance conditions were determined to be satisfied on February 24, 2025. These units are payable solely in shares of common stock, and remain subject to vesting on March 1, 2025.
Daniel V. Logue
2025-02-26