The most common and most likely answer to this crossword clue is the 4 plus 6 letter word LONG ISLAND
I've seen this crossword clue in The Daily Telegraph
L
O
N
G
I
S
L
A
N
D
Buddy explains!
The straight part
We know that "part of New York" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of new york = long island.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.