A right to be in US 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 us city?' is the wordplay.
'a right' becomes 'ar' (I've seen this in other clues).
'to be in' means one lot of letters goes inside another.
'us city?' becomes 'ny' (I've seen this in other clues).
'ar' placed within 'ny' is 'NARY'.
(Other definitions for nary that I've seen before include "Not spoken over there" , "Not in America" , "Never (a)" .)