Exhausted keeping new exhibition under wraps (9)
I believe the answer is:
unexposed
'under wraps' is the definition.
'exhausted keeping new exhibition' is the wordplay.
'exhausted' becomes 'used' (I've seen this before**).
'keeping' means one lot of letters goes inside another.
'new' becomes 'n'.
'exhibition' becomes 'expo' ('expo' can be a synonym of 'exhibition').
'n'+'expo'='nexpo'
'used' placed around 'nexpo' is 'UNEXPOSED'.
(Other definitions for unexposed that I've seen before include "Hidden" , "fully clothed?" , "Roundish handle" , "film not used" , "Closet" .)