For show, stripped during an exotic act (7)
I believe the answer is:
cabaret
'for show' is the definition.
(cabaret is a kind of show)
'stripped during an exotic act' is the wordplay.
'stripped' becomes 'bare' (synonyms).
'during' indicates putting letters inside.
'an exotic' indicates an anagram.
'act' is an anagram of 'cat'.
'bare' inserted into 'cat' is 'CABARET'.
(Other definitions for cabaret that I've seen before include "Floor-show as in nightclub" , "Variety entertainment" , "Bear cat (anag.)" , "Film set in 1931 Berlin - floor show" , "In nightspot" .)