Bank failing to open in cathedral city (3)
I believe the answer is:
ely
'cathedral city' is the definition.
(English city with a cathedral)
'bank failing to open' is the wordplay.
'bank' becomes 'rely' (to bank on something is to rely on it).
'failing to open' means to remove the first letter (the opening letter is removed).
'rely' with its initial letter taken away is 'ELY'.
'in' acts as a link.
(Other definitions for ely that I've seen before include "See" , "Small city in Cambridgeshire" , "Cambs diocese" , "Cambs. city" , "Cathedral city in Cambridgeshire" .)