The most common and most likely answer to this crossword clue is the 6 letter word FIGHTS
I've seen this crossword clue in The Guardian
F
I
G
H
T
S
Buddy explains!

The straight part
We know that "disputes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case disputes = fights.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 FIGHTS mean?
FIGHTS verb- To contend in physical conflict, either singly or in war, battle etc.
- To contend in physical conflict with each other, either singly or in war, battle etc.
- To strive for something; to campaign or contend for success.
- To conduct or engage in (battle, warfare etc.).
- To engage in combat with; to oppose physically, to contest with.
- To try to overpower; to fiercely counteract.
- To cause to fight; to manage or manoeuvre in a fight.
- Of colours or other design elements: to clash; to fail to harmonize.
- An occasion of fighting.
- A battle between opposing armies.
- A physical confrontation or combat between two or more people or groups.
- A boxing or martial arts match.
- A conflict, possibly nonphysical, with opposing ideas or forces; strife.
- The will or ability to fight.
- A screen for the combatants in ships.