Priest’s vestment not required, I hear (8)
I believe the answer is:
surplice
'priest's vestment' is the definition.
(vestment worn by a priest)
'not required i hear' is the wordplay.
'not required' becomes 'surplus'.
'i hear' shows a homophone (sound like).
'surplus' is a homophone of 'SURPLICE'.
(Other definitions for surplice that I've seen before include "White vestment worn over a cassock" , "Loose white vestment for clergy - sounds excessive?" , "Wide-sleeved white garment for clergy" , "Cure lips (anag)" , "Christian vestment" .)