The most common and most likely answer to this crossword clue is the 9 letter word QUENCHING
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Suppression" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suppression = quenching.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 QUENCHING mean?
QUENCHING verb- To satisfy, especially an actual or figurative thirst.
- To extinguish or put out (as a fire or light).
- To cool rapidly by dipping into a bath of coolant, as a blacksmith quenching hot iron.
- To terminate or greatly diminish (a chemical reaction) by destroying or deforming the remaining reagents.
- To rapidly change the parameters of a physical system.
- The extinction of any of several physical properties.
- The rapid cooling of a hot metal object, by placing it in a liquid, in order to harden it.