Relations love fair in New York (5)
I believe the answer is:
nooky
'relations' is the definition.
(both can mean sex)
'love fair in new york' is the wordplay.
'love' becomes 'o' (love means zero in tennis).
'fair' becomes 'ok'.
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
'o'+'ok'='ook'
'ook' going into 'ny' is 'NOOKY'.
(Other definitions for nooky that I've seen before include "Congress" , "Sexual activity (slang)" .)