The most common and most likely answer to this crossword clue is the 10 letter word MAGNIFYING
I've seen this crossword clue in The Guardian
M
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Buddy explains!
The straight part
We know that "exaggerating" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exaggerating = magnifying.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 MAGNIFYING mean?
MAGNIFYING verb- To praise, glorify (someone or something, especially God).
- To make (something) larger or more important.
- To make (someone or something) appear greater or more important than it is; to intensify, exaggerate.
- To make (something) appear larger by means of a lens, magnifying glass, telescope etc.
- To have effect; to be of importance or significance.