The most common and most likely answer to this crossword clue is the 3 letter word SHY
I've seen this crossword clue in The Guardian
S
H
Y
Buddy explains!

The straight part
We know that "quiet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quiet = shy.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 SHY mean?
SHY noun- An act of throwing.
- A place for throwing.
- A sudden start aside, as by a horse.
- In the Eton College wall game, a point scored by lifting the ball against the wall in the calx.
- To avoid due to timidness or caution.
- To jump back in fear.
- To throw sideways with a jerk; to fling
- Easily frightened; timid.
- Reserved; disinclined to familiar approach.
- Cautious; wary; suspicious.
- Short, insufficient or less than.
- Embarrassed.