Pressure concerning offer to claimant (9)
I believe the answer is:
pretender
'to claimant' is the definition.
(I've seen this before)
'pressure concerning offer' is the wordplay.
'pressure' becomes 'p' (abbreviation).
'concerning' becomes 're' (both can mean on a particular topic).
'offer' becomes 'tender' (tender can mean to offer something).
'p'+'re'+'tender'='PRETENDER'
(Other definitions for pretender that I've seen before include "One acting" , "One claiming a title" , "fake" , "Claimant, like Bonnie Prince Charlie" , "Claimant to a throne, usually without just title" .)