British bird in the city (5)
I believe the answer is:
berne
'the city' is the definition.
(Berne is an example)
'british bird' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'bird' becomes 'erne' (erne is a kind of bird).
'b'+'erne'='BERNE'
'in' acts as a link.
(Other definitions for berne that I've seen before include "Swiss capital" , "Swiss city (1886 copyright convention)" , "Capital of Switzerland" .)