A street in New York that’s not very nice (5)
I believe the answer is:
nasty
'not very nice' is the definition.
(I've seen this before)
'a street in new york' is the wordplay.
'street' becomes 'st' (abbreviation).
'in' means one lot of letters goes inside another.
'new york' becomes 'ny'.
'a'+'st'='ast'
'ast' going within 'ny' is 'NASTY'.
'that's' is the link.
(Other definitions for nasty that I've seen before include "Filthy" , "Disagreeable" , "Spiteful and unkind" , "Highly repugnant" , "grave" .)