Most put up with him (4)
I believe the answer is:
stan
'him' 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 off is 'STAN'.
'with' is the link.
(Other definitions for stan that I've seen before include "- Getz, jazz musician" , "- Laurel, Hardy's partner" , "One of the comic duo" , "Laurel and Hardy, . . . . and Ollie" , "Eminem hit; man's name" .)