Member of the clergy heading off shortly (4)
I believe the answer is:
anon
'shortly' is the definition.
(synonyms)
'member of the clergy heading off' is the wordplay.
'member of the clergy' becomes 'canon' (type of clergyman).
'heading off' means to remove the first letter.
'canon' with its first letter removed is 'ANON'.
(Other definitions for anon that I've seen before include "Without known author" , "Some time soon" , "Soon, in a little while" , "Of unknown name (abbr)" , "soon to be written" .)