Exasperated, miffed (6)
I believe the answer is:
peeved
This clue is a double definition.
'exasperated' is the first definition.
(thesaurus)
'miffed' is the second definition.
(thesaurus)
(Other definitions for peeved that I've seen before include "Irritated, vexed" , "Irritated, mildly annoyed" , "Annoyed, hacked off" , "Feeling irritated and out of sorts" , "Vexed, nettled" .)