The most common and most likely answer to this crossword clue is the 5 plus 1 plus 4 plus 2 plus 2 letter word MAKES A MEAL OF IT
I've seen this crossword clue in The Daily Telegraph
M
A
K
E
S
A
M
E
A
L
O
F
I
T
Buddy explains!
The straight part
We know that "Exaggerates" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exaggerates = makes a meal of it.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.