The most common and most likely answer to this crossword clue is the 4 plus 4 letter word TURN DOWN
I've seen this crossword clue in The Sunday Telegraph
T
U
R
N
D
O
W
N
More clues leading to the result TURN DOWN
- Refuse vessel originally donated in settlement
- Reject blue act appearing first
- . Depressed following act’s decline
- Refuse to fold over the sheet
- Tango drink covering container for refuse
- Go blue getting lower
- Reject performer on the spot
- Reject change, unhappy
- Refuse and go off depressed
- Refuse move out of order
Buddy explains!

The straight part
We know that "Reduce volume/refuse" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reduce volume/refuse = turn down.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.