Excuse one in vestment beside the writer (5)
I believe the answer is:
alibi
'excuse' is the definition.
(alibiing is a kind of excusing)
'one in vestment beside the writer' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' means one lot of letters goes inside another.
'vestment' becomes 'alb' (alb is a kind of vestment).
'beside' says to put letters next to each other (I've seen this in other clues).
'the writer' becomes 'i' (the person who is writing these clues).
'i' going inside 'alb' is 'alib'.
'alib'+'i'='ALIBI'
(Other definitions for alibi that I've seen before include "it may help you to get off" , "A claim one was elsewhere when crime took place" , "Claim put to court" , "Proof one was elsewhere when crime was committed" , "Defence against accusation - was seen elsewhere at the time" .)