The most common and most likely answer to this crossword clue is the 9 letter word VAINGLORY
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "boasting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case boasting = vainglory.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 VAINGLORY mean?
VAINGLORY noun- Excessive vanity.
- Boastful, unwarranted pride in one's accomplishments or qualities.
- Vain, ostentatious display.
- A regarding of oneself with undue favor.
- To boast; to act in a vain manner.