His cat let out for exercise (9)
I believe the answer is:
athletics
'for exercise' is the definition.
(thesaurus)
'his cat let out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'his'+'cat'+'let'='hiscatlet'
'hiscatlet' is an anagram of 'ATHLETICS'.
(Other definitions for athletics that I've seen before include "Oldham and Charlton?" , "Lithe acts observed in sporting contests" , "Lithe acts (anag)" , "Olympic sports" , "Running and jumping" .)