Irish premier (9)
I believe the answer is:
taoiseach
'irish premier' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for taoiseach that I've seen before include "Irish PM" , "Irish head of government" , "Leader of the government" , "Irish premier" , "I 'ate chaos (anag) - Irish Republic's prime minister" .)