Vestment returned by bishop let out (4)
I believe the answer is:
blab
'let out' is the definition.
(blabbing is a kind of letting out)
'vestment returned by bishop' is the wordplay.
'vestment' becomes 'alb' (alb is a kind of vestment).
'returned' says the letters should be written backwards.
'by' is a charade indicator (letters next to each other).
'bishop' becomes 'b' (abbreviation used in chess).
'alb' backwards is 'bla'.
'bla'+'b'='BLAB'
(Other definitions for blab that I've seen before include "Talk indiscreetly" , "Shoot one's mouth off" , "24 ac secrets in talk" , "Tells tales" , "Spill the beans" .)