Governor thinks they will accept direction (5)
I believe the answer is:
north
'direction' is the definition.
(compass direction)
'governor thinks they will accept' is the wordplay.
'will accept' indicates a hidden word.
'NORTH' can be found hidden inside 'governor thinks they'.
(Other definitions for north that I've seen before include "Thorn (anag.)" , "A 24 [STAR]" , "He let America go" , "usually featured at the top of the charts?" , "Arctic" .)