The most common and most likely answer to this crossword clue is the 4 plus 3 letter word RING OFF
I've seen this crossword clue in The Times
R
I
N
G
O
F
F
More clues leading to the result RING OFF
- Succeed in deposing leader — close call!
- What new divorcee could take to be cause of hang-up?
- Marriage evidently over? Don't say another word!
- Succeed in ignoring bit of blubbing and end the conversation
- Stop calling drummer loudly
- End call, engagement being cancelled?
- End call, evidently prepared for a divorce?
- Press cancel evidence of broken engagement
- No engaged signal, but put the phone down
- No longer married? Close call!
Buddy explains!

The straight part
We know that "Don't say another word!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case don't say another word! = ring off.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.