He's bound to seek a religious goal (7)
I believe the answer is:
'he's' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'bound to seek a religious goal' is the wordplay.
I cannot really see how this works, but
'bound' could be 'rim' (both can mean a limit or boundary) and 'rim' is found in the answer.
'religious' could be 'pi' (british abbreviation for pious) and 'pi' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pilgrim that I've seen before include "Traveller to a holy place" , "Mecca visitor" , "Wanderer" , "Traveller to shrine etc" , "traveller wanting to visit shrine" .)