Be left, to a degree, in control (6)
I believe the answer is:
remain
'be left' is the definition.
('remain' can be a synonym of 'be left')
'a degree in control' is the wordplay.
'a degree' becomes 'ma' (Master of Arts is a type of degree).
'in' means one lot of letters goes inside another.
'control' becomes 'rein' (rein is a kind of control).
'ma' going within 'rein' is 'REMAIN'.
'to' acts as a link.
(Other definitions for remain that I've seen before include "Stay on after others have gone" , "Stay, don't go" , "Stay around" , "Airmen (anag.)" , "Survive" .)