Bank not opening in cathedral city (3)
I believe the answer is:
ely
'cathedral city' is the definition.
(English city with a cathedral)
'bank not opening' is the wordplay.
'bank' becomes 'rely' (to bank on is to rely on).
'not opening' means to remove the first letter (the opening letter is removed).
'rely' with its first letter taken off is 'ELY'.
'in' is the link.
(Other definitions for ely that I've seen before include "Fenland city" , "Fenland cathedral town" , "Cambs. city" , "Diocese in Eastern England" , "Cambs diocese" .)