Support a quiet show (7)
I believe the answer is:
approve
'support' is the definition.
(I know that support is a more specific form of the action approve)
'a quiet show' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'show' becomes 'prove' (proving is a kind of showing).
'a'+'p'+'prove'='APPROVE'
(Other definitions for approve that I've seen before include "Regard with favour" , "Pass" , "Give thumbs-up to" , "Authorize" , "Give the nod to, sanction" .)