The most common and most likely answer to this crossword clue is the 12 letter word IMMODERATELY
I've seen this crossword clue in The Guardian
I
M
M
O
D
E
R
A
T
E
L
Y
Buddy explains!
The straight part
We know that "likely to act in a way that’s over the top" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case likely to act in a way that’s over the top = immoderately.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.