Put up with a girl in New York (8)
I believe the answer is:
brooklyn
'in new york' is the definition.
('Brooklyn' is part of 'new york')
'put up with a girl' is the wordplay.
'put up with' becomes 'brook' ('brook' can be a synonym of 'put up with').
'a girl' becomes 'lyn' (**).
'brook'+'lyn'='BROOKLYN'
(Other definitions for brooklyn that I've seen before include "New York area" , "New York borough with famous bridge." , "District and bridge in New York" , "Beckham Jr; NY borough" , "part of Long Island?" .)