Complicated tests on hat (7)
I believe the answer is:
stetson
'hat' is the definition.
(I know that Stetson is a type of hat)
'complicated tests on' is the wordplay.
'complicated' is an anagram indicator (a complex or confusing ordering of the letters).
'tests' anagrammed gives 'stets'.
'stets'+'on'='STETSON'
(Other definitions for stetson that I've seen before include "Tip" , "Hat, for Texan oil magnate, say" , "No tests (anag.)" , "Large hat" , "Ten-gallon hat" .)