As a student PPL in Ireland this is my understanding of the situation


If you hold an PPL from an ICAO contracting state, you can fly an
Irish registered aircraft in Ireland, under Visual Flight Rules (VFR).
However the only possible 'restriction' is that the flying club that
you rent the aircraft from will probably wish to conduct a short
checkride to make sure you can fly to their standards. Regardless of
any higher licenses or rating you may hold, though, you cannot fly
IFR.

However, if you are flying an aircraft registered in the same country
as you hold your license you can exercise the full privileges of that
license in Ireland, so for example, if you hold an American FAA ATP
you can fly IFR in Ireland on an N- reg aircraft.

For more complex inquiries contact the Irish Aviation Authority,
details below

Irish Aviation Authority,
Personnel Licensing,
Aviation House,
Hawkins Street,
Dublin 2.
www.iaa.ie

Phone +353 1 671 8655 Fax +353 1 679 2934