Peer is almost ahead of schedule (4)
I believe the answer is:
earl
'peer' is the definition.
(earl is a kind of peer)
'almost ahead of schedule' is the wordplay.
'almost' means to remove the last letter (almost the whole word is kept).
'ahead of schedule' becomes 'early' (I've seen this before).
'early' with its final letter taken off is 'EARL'.
'is' acts as a link.
(Other definitions for earl that I've seen before include "A real titled lord" , "Titled man" , "Noble title" , "Peer (Br.)" , "Aristocrat ranking between marquis and viscount" .)