Lean out of empty shack in New York (6)
I believe the answer is:
skinny
'lean' is the definition.
('skinny' can be similar in meaning to 'lean')
'empty shack in new york' is the wordplay.
'empty' says to hollow out the word (remove centre letters).
'new york' becomes 'ny'.
'shack' with its centre taken out is 'sk'.
'sk'+'in'+'ny'='SKINNY'
'out of' is the link.
(Other definitions for skinny that I've seen before include "Scrawny, underweight" , "Low-calorie white coffee -- sent any kilt (anag)" , "Spare: coffee with skimmed milk" , "Type of dip" , "Emaciated" .)