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

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-06-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001757898</issuerCik>
        <issuerName>STERIS plc</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001819129</rptOwnerCik>
            <rptOwnerName>Madsen Julia</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 70 SIR JOHN ROGERSON'S QUAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>2</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior VP, Life Sciences</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2023-06-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>43</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>202.42</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8969</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">43 shares were withheld from the 123 restricted shares that vested on June 1, 2023. These 43 shares represent the value of the taxes required to be withheld pursuant to applicable employment or tax laws, as determined by the Issuer. These 123 ordinary shares were awarded to Ms. Madsen on June 1, 2020. These vested shares were valued at the NYSE closing market price on June 1, 2023.</footnote>
        <footnote id="F2">As of June 1, 2023, 5,475 of these ordinary shares are restricted. The restrictions on these ordinary shares lapse as follows: 352 on June 2, 2023; 360 on June 2, 2023; 349 on October 2, 2023; 144 on October 2, 2023; 578 on May 31, 2024; 352 on June 3, 2024; 123 on June 3, 2024; 360 on June 3, 2024; 349 on October 1, 2024; 144 on October 1, 2024; 578 on June 2, 2025; 352 on June 2, 2025; 360 on June 2, 2025; 144 on October 1, 2025; 578 on June 1, 2026 and 352 on June 2, 2026.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ronald E. Snyder, Authorized Representative under Power of Attorney</signatureName>
        <signatureDate>2023-06-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
