A right to be in the city? Never! (4)
I believe the answer is:
nary
'never' is the definition.
(I've seen this in other clues)
'a right to be in the city?' is the wordplay.
'a right' becomes 'ar' (I've seen this in other clues).
'to be in the' indicates putting letters inside.
'city?' becomes 'ny' (I've seen this in other clues**).
'ar' inserted into 'ny' is 'NARY'.
(Other definitions for nary that I've seen before include "Not in America" , "Never (a)" , "Not spoken over there" .)