The most common and most likely answer to this crossword clue is the 9 letter word SURFEITED
I've seen this crossword clue in Financial Times
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More clues leading to the result SURFEITED
Buddy explains!

The straight part
We know that "filled to bursting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case filled to bursting = surfeited.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 SURFEITED mean?
SURFEITED verb- To fill (something) to excess.
- To feed (someone) to excess (on, upon or with something).
- To make (someone) sick as a result of overconsumption.
- To supply (someone) with something to excess; to disgust (someone) through overabundance.
- To satisfy (someone's appetite) to excess (both literally and figuratively).
- To overeat or feed to excess (on or upon something).
- To indulge (in something) to excess.
- To become sick from overindulgence (both literally and figuratively).