Relieved after Conservative quit (6)
I believe the answer is:
ceased
'quit' is the definition.
(I've seen this in another clue)
'relieved after conservative' is the wordplay.
'relieved' becomes 'eased' ('ease' can be a synonym of 'relieve').
'after' means one lot of letters go next to another.
'conservative' becomes 'C' (UK political abbreviation).
'eased' after 'c' is 'CEASED'.
(Other definitions for ceased that I've seen before include "Terminated" , "Came to an end" , "Concluded" , "Stopped, quit" , "Stopped, ended" .)