The most common and most likely answer to this crossword clue is the 7 letter word TERRORS
I've seen this crossword clue in The Daily Telegraph
T
E
R
R
O
R
S
More clues leading to the result TERRORS
Buddy explains!

The straight part
We know that "Mischievous brats" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mischievous brats = terrors.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 TERRORS mean?
TERRORS noun- Intense dread, fright, or fear.
- The action or quality of causing dread; terribleness, especially such qualities in narrative fiction.
- Something or someone that causes such fear.
- Terrorism