Person losing faith — a part of body has run out (8)
I believe the answer is:
apostate
'person' is the definition.
The answer is an example.
'losing faith a part of body has run out' is the wordplay.
I cannot really understand how this works, but
'a' is present in the answer.
'part' could be 'state' (I have seen 'Part of America' mean 'state' so perhaps 'part' could also mean 'state') and 'state' is found within the answer.
'of' could be 'o' and 'o' is found in the answer.
A single letter 'p' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for apostate that I've seen before include "One going to other side" , "Person who has renounced former belief" , "Defector" , "Person abandoning their religion" , "One losing faith" .)