Adolescent may end very small at New York; very small (5-5)
I believe the answer is:
teeny-weeny
'very small' is the definition.
(I've seen this in another clue)
'adolescent may end very small at new york' is the wordplay.
'adolescent' becomes 'teen' (teenager).
'end' says to take the final letters.
'very small' becomes 'wee' ('wee' is a Scottish word for small).
'at' is a charade indicator (letters next to each other).
'new york' becomes 'ny'.
The final letter of 'may' is 'y'.
'teen'+'y'+'wee'+'ny'='TEENY-WEENY'
(Other definitions for teeny-weeny that I've seen before include "Very small" , "Itsy-bitsy" , "Minuscule" , "Minute" .)