The most common and most likely answer to this crossword clue is the 9 letter word MARTYRDOM
I've seen this crossword clue in The Guardian
M
A
R
T
Y
R
D
O
M
Buddy explains!

The straight part
We know that "Suffering" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suffering = martyrdom.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 MARTYRDOM mean?
MARTYRDOM noun- The condition of a martyr; the death of a martyr; the suffering of death on account of adherence to the Christian faith, or to any cause.
- Extreme suffering, affliction; torment; torture, especially without reason.