Voiced one's irritation at department (5)
I believe the answer is:
aired
'voiced' is the definition.
(as in airing one's views)
'one's irritation at department' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'irritation' becomes 'ire' (ire can mean anger).
'at' is a charade indicator (letters next to each other).
'department' becomes 'd' (abbreviation eg in MOD Ministry of Defence).
'a'+'ire'+'d'='AIRED'
(Other definitions for aired that I've seen before include "Exposed to breeze for freshening - say damp clothes" , "Vented to or exposed to breeze" , "Ventilated, or hung out to dry" , "Put to dry; said publicly" , "Made public" .)