The most common and most likely answer to this crossword clue is the 9 letter word DYSPEPTIC
I've seen this crossword clue in The Guardian
D
Y
S
P
E
P
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I
C
More clues leading to the result DYSPEPTIC
Buddy explains!

The straight part
We know that "Suffering indigestion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suffering indigestion = dyspeptic.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 DYSPEPTIC mean?
DYSPEPTIC noun- A dyspeptic person.
- Of, relating to, or having dyspepsia or indigestion.
- Irritable or morose.