The most common and most likely answer to this crossword clue is the 4 letter word JOSH
I've seen this crossword clue in Independent
J
O
S
H
Buddy explains!

The straight part
We know that "kid" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kid = josh.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.
What does JOSH mean?
JOSH noun- An instance of good-natured banter.
- To tease someone in a kindly or friendly fashion.
- To make or exchange good-natured jokes.