Peer almost ahead of schedule (4)
I believe the answer is:
earl
'peer' is the definition.
(I know that earl is a type 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'.
(Other definitions for earl that I've seen before include "Peer (Br.)" , "Sandwich perhaps" , "Rank below marquess" , "Aristocrat ranking between marquis and viscount" , "A lord like Lear" .)