The most common and most likely answer to this crossword clue is the 10 letter word SOUNDPROOF
I've seen this crossword clue in The Daily Telegraph
S
O
U
N
D
P
R
O
O
F
More clues leading to the result SOUNDPROOF
Buddy explains!

The straight part
We know that "Make quiet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make quiet = soundproof.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 SOUNDPROOF mean?
SOUNDPROOF verb- To make resistant to transmitting sound.
- Not allowing sound through.