The most common and most likely answer to this crossword clue is the 7 letter word PLUGGED
I've seen this crossword clue in The Daily Telegraph
P
L
U
G
G
E
D
More clues leading to the result PLUGGED
Buddy explains!

The straight part
We know that "Carried on quietly, perhaps?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case carried on quietly, perhaps? = plugged.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 PLUGGED mean?
PLUGGED verb- To stop with a plug; to make tight by stopping a hole.
- To blatantly mention a particular product or service as if advertising it.
- To persist or continue with something.
- To shoot a bullet into something with a gun.
- To have sex with, penetrate sexually.