Most put up with this chap (4)
I believe the answer is:
stan
'this chap' is the definition.
'most put up' is the wordplay.
'most' means to remove the last letter.
'put up' becomes 'stand' (I've seen this before).
'stand' with its last letter taken away is 'STAN'.
'with' is the link.
(Other definitions for stan that I've seen before include "Laurel perhaps" , "One of the comic duo" , "- Laurel, Hardy's partner" , "- Laurel, comedian" , "Eminem hit; man's name" .)