Quietly increase approval (6)
I believe the answer is:
praise
'approval' is the definition.
(praise is a kind of approval)
'quietly increase' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'increase' becomes 'raise' (raise can mean to increase or put up).
'p'+'raise'='PRAISE'
(Other definitions for praise that I've seen before include "Aspire (anag)" , "Express approval and admiration" , "Cry 'hallelujah'" , "Commendation" , "Speak highly of" .)