saying your flying from the US to the UK and you have an FAA licence, you can do so on your FAA licence prividing you fly a US aircraft (therefore N reg). if say you were doing the same trip but in a british aircraft you will need a UK licence.
if you have done your training in the UK and have a UK CAA licence but get a job in Ireland you will need to convert your licence wich generaly means paper work and handing a wad of cash over. however every country has different licence cirteria so some may require some more training. i know converting from a UK licence to an FAA one all it is is some paperwork but the other way around you will need to redo your CPL and IR.