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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2024-02-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001847572</rptOwnerCik>
            <rptOwnerName>White Jay</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3015 CARRINGTON MILL BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MORRISVILLE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>27560</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CVP &amp; Pres, Global Commercial</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-02-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>251</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4843</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </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 19, 2024. These units are payable solely in shares of common stock, and remain subject to vesting on March 2, 2024.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Daniel V. Logue with POA for Jay White</signatureName>
        <signatureDate>2024-02-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wk-form4_1708563794.xml", "description": "FORM 4", "secsgml_size_bytes": 3400}]
X0508
4
2024-02-19
0
0000096943
TELEFLEX INC
TFX
0001847572
White Jay
3015 CARRINGTON MILL BLVD.
MORRISVILLE
NC
27560
0
1
0
0
CVP & Pres, Global Commercial
0
Common Stock
2024-02-19
4
A
0
251
0
A
4843
D
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 19, 2024. These units are payable solely in shares of common stock, and remain subject to vesting on March 2, 2024.
Daniel V. Logue with POA for Jay White
2024-02-21