The most common and most likely answer to this crossword clue is the 4 plus 7 letter word YOOF CULTURE
I've seen this crossword clue in The Guardian
Y
O
O
F
C
U
L
T
U
R
E
Buddy explains!
The straight part
We know that "Kids’ style" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kids’ style = yoof culture.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.