Left in the ladies' quarters, somewhere in New York (6)
I believe the answer is:
harlem
'in new york' is the definition.
('Harlem' is part of 'new york')
'left in the ladies' quarters somewhere' is the wordplay.
I cannot really understand how this works, but
'left' could be 'l' (common abbreviation) and 'l' is found in the answer.
'quarters' could be 'harem' (harem is a kind of quarters) and 'harem' is found within the remaining letters.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for harlem that I've seen before include "'District of Manhattan, noted for jazz clubs (6)'" , "Father (French)" , "NY community" , "some of the Big Apple" , "Part of New York City" .)