I am in a similar situation as I just moved from the UK to Ireland and am remaining with my UK employer as a remote worker. I can find no clear answer on how taxation should be handled.
Be wary of the guidance document "Moving to Ireland" in the
Revenue FAQ as it has not been updated for 5 years since which there has been legislation ending the remittance basis of taxation.
My company employed some taxation lawyers in Dublin who's advice was
"the general rule now is that irrespective of the residence or domicile position of an individual such income attributable to the performance in the State of duties of such officer or employment, where the individual spends in excess of 60 days in the State are within the scope of PAYE"
They further advised that whether I am paid in £ to my UK bank or € to my Irish bank my UK employer needs to register with the Revenue commissioner for PAYE. In my case my employer refuses to do this which leaves me in a rather awkward position.
There are some huge anomolies between the laws of UK and ROI - According to UK tax authorities I should pay UK tax as I haven't been out of the UK for more than 183 days.
According to the Irish tax office I should pay Irish taxes as I've now worked in Ireland for more than 60 days.
I now read that in the last budget the remittance basis of taxation was reinstated for UK sourced income after pressure from the EU. I'm hoping that this means my UK employer can pay my salary gross and let me sort out my tax personally as if I were self employed.
I've contacted both the UK and Irish tax offices, given them the same information and asked them to sort it out.
If and when I get an answer I'll post it here.... although I may be drawing my pension by then