Cathedral clergy dispensing with clothing shortly (4)
I believe the answer is:
anon
'shortly' is the definition.
(synonyms)
'cathedral clergy dispensing with clothing' is the wordplay.
'cathedral clergy' becomes 'canons' (canon is a type of clergyman).
'dispensing with clothing' indicates the central letters (letters which clothe the word are removed).
The centre of 'canons' is 'ANON'.
(Other definitions for anon that I've seen before include "Soon, in a little while" , "Of unknown name (abbr)" , "Nameless (abbr.); soon" , "prolific author" , "Presently - unattributed" .)