Claimant is quiet about offer (9)
I believe the answer is:
pretender
'claimant' is the definition.
(I know that Pretender is a type of claimant)
'quiet about offer' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'about' becomes 're' ('re' means regarding or about).
'offer' becomes 'tender' (tender can mean to offer something).
'p'+'re'+'tender'='PRETENDER'
'is' acts as a link.
(Other definitions for pretender that I've seen before include "One acting" , "One who claims a title or position" , "Claimant, like Bonnie Prince Charlie" , "fake" , "One claiming a title" .)