The most common and most likely answer to this crossword clue is the 9 letter word PNEUMATIC
I've seen this crossword clue in Financial Times
P
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The straight part
We know that "all puffed up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case all puffed up = pneumatic.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 PNEUMATIC mean?
PNEUMATIC noun- A vehicle, such as a bicycle, whose wheels are fitted with pneumatic tyres.
- (gnosticism) In the gnostic theologian Valentinus' triadic grouping of man, the highest type; a person focused on spiritual reality (the other two being hylic and psychic).
- Of, relating to, or resembling air or other gases
- Of or relating to pneumatics
- Powered by, or filled with, compressed air
- Having cavities filled with air
- Spiritual; of or relating to the pneuma
- (of a woman) well-rounded; full-breasted; bouncy