You cannot generally claim exemption from the payment of Irish income tax if you are a PAYE worker in the Republic simply because you reside in the north/UK.   As a UK resident with earnings that arise outside of the UK you are obliged to complete a return of that income to Revenue in the north under self-assessment rules. You should be given a credit or relief in respect of any Irish income tax you are paying because of the double taxation agreement between the Republic and the UK.  There may or may not be a balance of income tax to pay to Revenue in the north.  This means that there may be tax payable to Revenue in the north as well as to Revenue in the south.