Irish king a few will find exasperating? (7)
I believe the answer is:
irksome
'exasperating?' is the definition.
(thesaurus)
'irish king a few' is the wordplay.
'irish' becomes 'Ir' (abbreviation).
'king' becomes 'k' (abbreviation for king in chess).
'a few' becomes 'some' (I've seen this before).
'ir'+'k'+'some'='IRKSOME'
'will find' acts as a link.
(Other definitions for irksome that I've seen before include "Smokier (anag.)" , "Smoker I find annoying" , "Annoying or tiresome" , "'Tedious, tiresome (7)'" , "'Annoying, irritating or boring (7)'" .)