The most common and most likely answer to this crossword clue is the 8 plus 1 letter word ADIPOSE} –
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "Fat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fat = adipose} –.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 ADIPOSE} – mean?
ADIPOSE} – noun- Animal fat stored in the tissue of the body.
- Containing, composed of, or consisting of fat; fatty.
- Slightly overweight; chubby.