Greater than governor over North Dakota (6)
I believe the answer is:
beyond
'greater than' is the definition.
(beyond can mean greater than or larger than)
'governor over north dakota' is the wordplay.
'governor' becomes 'bey' (bey is a kind of governor).
'over north dakota' becomes 'ond' (this might be a standard abbreviation I've not previously seen).
'bey'+'ond'='BEYOND'
(Other definitions for beyond that I've seen before include "Past" , "Farther along in space, time or degree" , "On the far side of" , "Farther than or outside" , "unknown" .)