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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001559053</issuerCik>
        <issuerName>Prothena Corp plc</issuerName>
        <issuerTradingSymbol>PRTA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001564380</rptOwnerCik>
            <rptOwnerName>Kinney Gene G.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PROTHENA BIOSCIENCES INC</rptOwnerStreet1>
            <rptOwnerStreet2>650 GATEWAY BOULEVARD</rptOwnerStreet2>
            <rptOwnerCity>SOUTH SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CSO &amp; Head of R&amp;D</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>30000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.41</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32793</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>8201</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>65.4616</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24592</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20439</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>66.3724</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4153</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1360</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>67.0517</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2793</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>6.41</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-12-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>30000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2023-01-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>170000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The sale reported in the Form 4 was effected pursuant to a Rule 10b5 1 trading plan adopted by the Reporting Person.</footnote>
        <footnote id="F2">The transaction was executed in multiple trades in prices ranging from $64.83 to $65.82, inclusive.  The price reported in Column 4 above reflects the weighted average sale price.  The Reporting Person hereby undertakes to provide upon request to the SEC staff, the Issuer, or a stockholder of the Issuer, information regarding the number of shares and prices at which the transaction was effected.</footnote>
        <footnote id="F3">The transaction was executed in multiple trades in prices ranging from $65.83 to $66.82, inclusive.  The price reported in Column 4 above reflects the weighted average sale price.  The Reporting Person hereby undertakes to provide upon request to the SEC staff, the Issuer, or a stockholder of the Issuer, information regarding the number of shares and prices at which the transaction was effected.</footnote>
        <footnote id="F4">The transaction was executed in multiple trades in prices ranging from $66.83 to $67.54, inclusive.  The price reported in Column 4 above reflects the weighted average sale price.  The Reporting Person hereby undertakes to provide upon request to the SEC staff, the Issuer, or a stockholder of the Issuer, information regarding the number of shares and prices at which the transaction was effected.</footnote>
        <footnote id="F5">The shares subject to the option will vest and become exercisable as to 25% of the total number of shares subject to the option on January 29, 2014 and with respect to 1/48th of the total number of shares subject to the option in successive, equal monthly installments on each monthly anniversary thereafter, subject to the Reporting Person's continued employment with the Issuer on each such vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ A.W. Homan, as Attorney-in-Fact for Gene G. Kinney</signatureName>
        <signatureDate>2015-12-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
