When resident outside of EU and contracting for an Irish company as a director of an umbrella company setup by accounting provider in Ireland should one be paying tax in Ireland?
I'm sure your accounting provider will be able to provide some assistance to you on this matter.
For some background reading, have a look at page 21 "Non-resident directors of Irish incorporated companies" of this guidance note from Irish Revenue to see if it is of relevance to your situation:
Perhaps provide a few more details (what country are you tax resident in, proposed form of remuneration from your company, are you talking about income tax/corporation tax/capital taxes etc.) so that those members on here qualified in tax can provide some useful feedback.