Write to New York for her (5)
I believe the answer is:
penny
'her' is the definition.
'write to new york' is the wordplay.
'write' becomes 'pen' (synonyms).
'to new york' becomes 'ny'.
'pen'+'ny'='PENNY'
'for' acts as a link.
(Other definitions for penny that I've seen before include "Coin - girl's name" , "Lancaster" , "Girl" , "One hundredth of a pound" , "p; small coin" .)