The most common and most likely answer to this crossword clue is the 8 letter word BROOKLYN
I've seen this crossword clue in The Guardian
B
R
O
O
K
L
Y
N
More clues leading to the result BROOKLYN
- Bear with wild cat killing ten in New York area
- Girl under water in populous borough
- Bird eaten by black tailless cat somewhere in Kings
- Accept New York location’s first to come up – for this place?
- Borough of Hamlyn cut in two by beck
- Tolerate large, upwardly mobile, New York borough
- Posh kid has to tolerate travel by train, all may conclude
- Bishop and other man left New York, over part of the city
- Black bird extremely lucky to land on new bridge, for one
- Bear left, reaching westerly city borough
Buddy explains!

The straight part
We know that "Posh kid/Posh kid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case posh kid/posh kid = brooklyn.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.