Competitor makes prisoner an offer (9)
I believe the answer is:
contender
'competitor' is the definition.
(synonyms)
'prisoner an offer' is the wordplay.
'prisoner' becomes 'con' (abbreviation for 'convict').
'an offer' becomes 'tender' (tender can mean to offer something).
'con'+'tender'='CONTENDER'
'makes' is the link.
(Other definitions for contender that I've seen before include "Candidate" , "Competitor, challenger" , "one in the field" , "One striving" , "Struggler in rivalry" .)