Give encouragement to holy person leaving diocese (5)
I believe the answer is:
cheer
'give encouragement to' is the definition.
(cheer can mean to encourage or gladden)
'holy person leaving diocese' is the wordplay.
'holy person' becomes 'st' (short for saint).
'leaving' is a deletion indicator.
'diocese' becomes 'chester' (I've seen this before).
'chester' with 'st' taken out is 'CHEER'.
(Other definitions for cheer that I've seen before include "hurrah" , "Fare" , "Shout applause and support" , "Encouraging shout" , "Buck up" .)