Left in women's quarters in Manhattan area (6)
I believe the answer is:
harlem
'manhattan area' is the definition.
(I've seen this in another clue)
'left in women's quarters' is the wordplay.
'left' becomes 'l' (common abbreviation).
'in' is an insertion indicator.
'women's quarters' becomes 'harem' (historically, women's quarters in Muslim household).
'l' placed inside 'harem' is 'HARLEM'.
'in' is the link.
(Other definitions for harlem that I've seen before include "Area of New York city" , "NY community" , "Part of New York City" , "some of the Big Apple" , "Father (French)" .)