Soft object to exhibit (7)
I believe the answer is:
present
'exhibit' is the definition.
(I know that exhibit can be written as present)
'soft object to' is the wordplay.
'soft' becomes 'p' (musical abbreviation for piano, 'soft').
'object to' becomes 'resent' (to resent something is to dislike it).
'p'+'resent'='PRESENT'
(Other definitions for present that I've seen before include "gift > offer" , "A Christmas gift" , "Current" , "Christmas hand-out" , "Repents (anag.)" .)