To finish the job, I had an offer (3)
I believe the answer is:
bid
'an offer' is the definition.
(bid is a kind of offer)
'to finish the job i had' is the wordplay.
'to finish' says to take the final letters.
'i had' becomes 'i'd' (I'd).
The final letter of 'job' is 'b'.
'b'+'id'='BID'
(Other definitions for bid that I've seen before include "Invite" , "Try" , "Make an offer at auction" , "Tender (for work)" , "Take part in auction" .)