The most common and most likely answer to this crossword clue is the 6 letter word DETACH
I've seen this crossword clue in The Guardian
D
E
T
A
C
H
More clues leading to the result DETACH
- Didn't like touring Croatia's capital, back in Split
- Release cadet, excited at start of holiday
- Free wild animal man had brought round about
- . Watched in agony after losing wife in divorce
- Set free, leader of coup in deeply unpopular revolutionary
- Separate bidet
- To get unengaged, the chap had to take Kitty back
- The cad is out to break the engagement
- Part the cad needed to play
- Teach daughter another way to take away
Buddy explains!

The straight part
We know that "break the engagement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case break the engagement = detach.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 DETACH mean?
DETACH verb- To take apart from; to take off.
- To separate for a special object or use.
- To come off something.