The most common and most likely answer to this crossword clue is the 8 letter word SPLIT-UP
S
P
L
I
T
-
U
P
More clues leading to the result SPLIT-UP
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 = split-up.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 SPLIT-UP mean?
SPLIT-UP noun- A break-up.