He would have you believe he’s had a previous offer (9)
I believe the answer is:
pretender
'he would have you believe he's' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'a previous offer' is the wordplay.
'a previous' becomes 'pre' (I can't explain this - if you can you should give a lot more credence to this answer).
'offer' becomes 'tender' (tender can mean to offer something).
'pre'+'tender'='PRETENDER'
'had' is the link.
Can you help me to learn more?
(Other definitions for pretender that I've seen before include "One who claims a title or position" , "Claimant to a throne, usually without just title" , "fake" , "One claiming a title" , "One acting" .)