A non-drinker, he is at heart an unbeliever (7)
I believe the answer is:
atheist
'an unbeliever' is the definition.
(atheist is a kind of unbeliever)
'a non-drinker he is at heart' is the wordplay.
'non drinker' becomes 'tt' (abbreviation for teetotaller).
'at heart' indicates putting letters inside (inserted letters go to the heart of the word).
'he'+'is'='heis'
'tt' going around 'heis' is 'theist'.
'a'+'theist'='ATHEIST'
(Other definitions for atheist that I've seen before include "One denying existence of a god" , "Person who believes there is no God" , "Non-believer in god - hates it (anag)" , "Godless person" , "Person who does not believe in existence of a god" .)