Member of the clergy caught out immediately (4)
I believe the answer is:
anon
'immediately' is the definition.
(I've seen this before)
'member of the clergy caught out' is the wordplay.
'member of the clergy' becomes 'canon' (I've seen this before).
'caught' becomes 'c' (cricket abbreviation).
'out' indicates named letters should be taken away.
'canon' with 'c' taken away is 'ANON'.
(Other definitions for anon that I've seen before include "Shortly; unknown" , "Soon - nobody knows me" , "before long" , "In due course" , "Presently - or unknown" .)