Depend on having registered at cathedral city (4)
I believe the answer is:
rely
'depend' is the definition.
(to depend on someone is to rely on them)
'registered at cathedral city' is the wordplay.
'registered' becomes 'R' (abbreviation, as in registered trademark).
'at' is a charade indicator (letters next to each other).
'cathedral city' becomes 'Ely' (English city with a cathedral).
'r'+'ely'='RELY'
'on having' acts as a link.
(Other definitions for rely that I've seen before include "Depend, bank" , "Be sure" , "Old rally" , "Lyre (anag.)" , "Trust, depend" .)