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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2024-05-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001236161</rptOwnerCik>
            <rptOwnerName>HAGGERTY GRETCHEN R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 550 E. SWEDESFORD ROAD, SUITE 400</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WAYNE</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19087</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>649</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4754</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option / (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>201.52</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2024-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1349</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2025-05-07</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2034-05-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1349</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1349</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted Stock Unit Award granted pursuant to the Teleflex Incorporated 2023 Stock Incentive Plan. Award vests on the one-year anniversary of the grant date; provided, however, if the reporting person does not stand for re-election to the issuer's board of directors at the issuer's 2025 annual meeting of stockholders (the &quot;2025 Annual Meeting&quot;), the award will vest on the earlier of the one-year anniversary of the grant date and the date of the 2025 Annual Meeting, so long as such meeting is held at least 50 weeks after the issuer's 2024 annual meeting of stockholders.</footnote>
        <footnote id="F2">If the reporting person does not stand for re-election to the issuer's board of directors at the issuer's 2025 annual meeting of stockholders (the &quot;2025 Annual Meeting&quot;), the award will vest on the earlier of the one-year anniversary of the grant date and the date of the 2025 Annual Meeting, so long as such meeting is held at least 50 weeks after the issuer's 2024 annual meeting of stockholders.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Daniel V. Logue with POA for Gretchen R. Haggerty</signatureName>
        <signatureDate>2024-05-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0508
4
2024-05-07
0
0000096943
TELEFLEX INC
TFX
0001236161
HAGGERTY GRETCHEN R
C/O 550 E. SWEDESFORD ROAD, SUITE 400
WAYNE
PA
19087
1
0
0
0
0
Common Stock
2024-05-07
4
A
0
649
0
A
4754
D
Stock Option / (Right to Buy)
201.52
2024-05-07
4
A
0
1349
0
A
2025-05-07
2034-05-07
Common Stock
1349
1349
D
Restricted Stock Unit Award granted pursuant to the Teleflex Incorporated 2023 Stock Incentive Plan. Award vests on the one-year anniversary of the grant date; provided, however, if the reporting person does not stand for re-election to the issuer's board of directors at the issuer's 2025 annual meeting of stockholders (the "2025 Annual Meeting"), the award will vest on the earlier of the one-year anniversary of the grant date and the date of the 2025 Annual Meeting, so long as such meeting is held at least 50 weeks after the issuer's 2024 annual meeting of stockholders.
If the reporting person does not stand for re-election to the issuer's board of directors at the issuer's 2025 annual meeting of stockholders (the "2025 Annual Meeting"), the award will vest on the earlier of the one-year anniversary of the grant date and the date of the 2025 Annual Meeting, so long as such meeting is held at least 50 weeks after the issuer's 2024 annual meeting of stockholders.
Daniel V. Logue with POA for Gretchen R. Haggerty
2024-05-09