Heathen state taken by Greek god (5)
I believe the answer is:
pagan
'heathen' is the definition.
(both can mean an irreligious person)
'state taken by greek god' is the wordplay.
'state' becomes 'ga' (abbreviation for the US state).
'taken by' indicates putting letters inside.
'greek god' becomes 'Pan' (Pan is an example).
'ga' placed within 'pan' is 'PAGAN'.
(Other definitions for pagan that I've seen before include "One who does not acknowledge your god(s)" , "One who does not acknowledge a god" , "Unchristian" , "Infidel" , "Person without any conventional religion" .)