A doubter disheartened an abstainer (7)
I believe the answer is:
ascetic
'an abstainer' is the definition.
('ascetic' can be a synonym of 'abstainer')
'a doubter disheartened' is the wordplay.
'doubter' becomes 'sceptic' (synonyms).
'disheartened' says to hollow out the word (remove centre letters) (the middle or heart is removed).
'sceptic' with its centre taken out is 'scetic'.
'a'+'scetic'='ASCETIC'
(Other definitions for ascetic that I've seen before include "Mortifying the flesh" , "Austere, abstinent" , "reclusive" , "Self-disciplined person" , "Austere, Spartan" .)