Finished in government (4)
I believe the answer is:
over
'finished' is the definition.
('over' can be similar in meaning to 'finished')
'in government' is the wordplay.
'in' indicates a hidden word.
'OVER' is hidden within 'government'.
(Other definitions for over that I've seen before include "A bowler's round in cricket" , "Finished like cricket session" , "superior position" , "Work out of hours" , "Completely ended" .)