State of silent exasperation (5)
I believe the answer is:
texas
'state' is the definition.
(Texas is an example)
'of silent exasperation' is the wordplay.
'of' indicates a hidden word.
'TEXAS' can be found hidden inside 'silent exasperation'.
(Other definitions for texas that I've seen before include "Austin's state" , "Second-largest US state by area" , "Breed of cattle -- non-Goths relax (anag)" , "America's Lone Star State" , "State on the Gulf of Mexico" .)