The most common and most likely answer to this crossword clue is the 7 letter word STILLER
I've seen this crossword clue in The Times
S
T
I
L
L
E
R
Buddy explains!

The straight part
We know that "Quieter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quieter = stiller.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 STILLER mean?
STILLER adjective- Not moving; calm.
- Not effervescing; not sparkling.
- Uttering no sound; silent.
- Having the same stated quality continuously from a past time
- Comparatively quiet or silent; soft; gentle; low.
- Constant; continual.
- One who stills, or quiets.