Rule Conservative must leave promptly (4)
I believe the answer is:
anon
'promptly' is the definition.
(anon can mean soon or promptly)
'rule conservative must leave' is the wordplay.
'rule' becomes 'canon' (canon is a kind of rule).
'conservative' becomes 'C' (UK political abbreviation).
'must leave' indicates named letters should be taken away.
'canon' with 'c' taken away is 'ANON'.
(Other definitions for anon that I've seen before include "Mystery writer" , "prolific author" , "Soon, precious stone" , "Presently - or unknown" , "Without known author" .)