Competitor gives prisoner offer (9)
I believe the answer is:
contender
'competitor' is the definition.
('contender' can be a synonym of 'competitor')
'prisoner offer' is the wordplay.
'prisoner' becomes 'con' (abbreviation for 'convict').
'offer' becomes 'tender' (tender offer is a kind of offer).
'con'+'tender'='CONTENDER'
'gives' is the link.
(Other definitions for contender that I've seen before include "Competitor, challenger" , "Struggler in rivalry" , "One seeking title" , "One striving" , "No red cent (anag.)" .)