Quietly feel bitter about award (7)
I believe the answer is:
present
'award' is the definition.
('present' can be a synonym of 'award')
'quietly feel bitter about' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'feel bitter about' becomes 'resent' ('resent' can be a synonym of 'feel bitter about').
'p'+'resent'='PRESENT'
(Other definitions for present that I've seen before include "available" , "able to be registered" , "Gift; time now; here" , "in a particular place" , "A Christmas gift" .)