The most common and most likely answer to this crossword clue is the 2 plus 4 plus 3 plus 4 plus 2 letter word GO AWAY AND SHUT UP
I've seen this crossword clue in The Guardian
G
O
A
W
A
Y
A
N
D
S
H
U
T
U
P
Buddy explains!

The straight part
We know that "we don’t want to hear any more" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case we don’t want to hear any more = go away and shut up.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.