The most common and most likely answer to this crossword clue is the 3 plus 5 letter word RED ROVER
R
E
D
R
O
V
E
R
More clues leading to the result RED ROVER
Buddy explains!

The straight part
We know that "Children’s game" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case children’s game = red rover.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.