The most common and most likely answer to this crossword clue is the 10 letter word UNEVENTFUL
I've seen this crossword clue in The Guardian
U
N
E
V
E
N
T
F
U
L
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 = uneventful.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 UNEVENTFUL mean?
UNEVENTFUL adjective- Monotonous; lacking significant or noteworthy events