Regretted admitting Left governed (5)
I believe the answer is:
ruled
'governed' is the definition.
('rule' can be a synonym of 'govern')
'regretted admitting left' is the wordplay.
'regretted' becomes 'rued' ('rue' can be a synonym of 'regret').
'admitting' indicates putting letters inside.
'left' becomes 'l' (common abbreviation).
'rued' placed around 'l' is 'RULED'.
(Other definitions for ruled that I've seen before include "Reigned or ordered" , "Made authoritative statement" , "Reigned - lined - decided" , "Were tops" , "Governed - with lines" .)