The most common and most likely answer to this crossword clue is the 8 letter word LITIGATE
I've seen this crossword clue in The Guardian
L
I
T
I
G
A
T
E
More clues leading to the result LITIGATE
- Initially losing it, then irritated, spectators take legal action
- Sue‘s books, one with a scandalous ending
- Had settled game with it before dispute
- Take action in individual drinker’s scandal?
- Sue settled on one way in
- Take up a case set down by one departure point
- Sue? Mark? It turned into romance
- Sue that is holding gun, fired earlier
- Take action in case?
- Press charges untruth about titanium revolver
Buddy explains!

The straight part
We know that "dispute" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dispute = litigate.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 LITIGATE mean?
LITIGATE verb- (construed with on) To go to law; to carry on a lawsuit.
- To contest in law.
- (transferred sense) To dispute; to fight over.