The most common and most likely answer to this crossword clue is the 9 letter word NICKERING
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Buddy explains!

The straight part
We know that "laughing quietly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case laughing quietly = nickering.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 NICKERING mean?
NICKERING verb- To make a soft neighing sound characteristic of a horse.
- To produce a snigger or suppressed laugh.
- The sound of a horse that nickers.