The most common and most likely answer to this crossword clue is the 9 letter word BETROTHED
I've seen this crossword clue in Independent
B
E
T
R
O
T
H
E
D
Buddy explains!

The straight part
We know that "Engaged" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case engaged = betrothed.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 BETROTHED mean?
BETROTHED verb- To promise to give in marriage.
- To promise to take (as a future spouse); to plight one's troth to.
- One who is betrothed, i.e. a fiancé or fiancée.
- Engaged to be married.