Person of faith indulged, essentially (5)
I believe the answer is:
hindu
'person' is the definition.
(Hindu is an example)
'of faith indulged essentially' is the wordplay.
'of' indicates a hidden word.
'HINDU' can be found hidden inside 'faith indulged essentially'.
(Other definitions for hindu that I've seen before include "Devotee of Indian religion" , "One practising an Indian religion" , "Person belonging to major Indian religion" , "Adherent of an eastern religion" , "Adherent of an Asian religion" .)