Peer is almost premature (4)
I believe the answer is:
earl
'peer' is the definition.
(I know that earl is a type of peer)
'almost premature' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'premature' becomes 'early' (similar in meaning).
'early' with its final letter removed is 'EARL'.
'is' is the link.
(Other definitions for earl that I've seen before include "Jimmy Carter's middle name" , "Sandwich perhaps" , "British noble" , "Noble title" , "A real sort of lord" .)