The most common and most likely answer to this crossword clue is the 3 plus 1 plus 4 letter word NOT A PEEP
I've seen this crossword clue in Independent
N
O
T
A
P
E
E
P
More clues leading to the result NOT A PEEP
- Pen a poet ruined: say nothing!
- Switching on cassette, record silence
- Upset about recording – old recording having no sound
- No recordings, no sound
- No cassette and vinyl recording, no sound at all
- Bandage plugging open wound causes calmness
- The Sound of Silence – number on cassette and vinyl?
- Nothing to listen to on playing back band’s record
- Silent, unlike a shepherdess?
- Be quiet and no looking!
Buddy explains!

The straight part
We know that "having no sound" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having no sound = not a peep.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.