The most common and most likely answer to this crossword clue is the 10 letter word SEPARATION
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More clues leading to the result SEPARATION
Buddy explains!

The straight part
We know that "divorce" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case divorce = separation.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 SEPARATION mean?
SEPARATION noun- The act of disuniting two or more things, or the condition of being separated.
- The act or condition of two or more people being separated from one another.
- The act or condition of a married couple living in separate homes while remaining legally married.
- The place at which a division occurs.
- An interval, gap or space that separates things or people.
- An object that separates two spaces.
- Departure from active duty, while not necessarily leaving the service entirely.