The most common and most likely answer to this crossword clue is the 10 letter word CONTENTION
C
O
N
T
E
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Buddy explains!

The straight part
We know that "Dispute/claim" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dispute/claim = contention.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 CONTENTION mean?
CONTENTION noun- Argument, contest, debate, strife, struggle.
- A point maintained in an argument, or a line of argument taken in its support; the subject matter of discussion of strife; a position taken or contended for.
- Competition by parts of a system or its users for a limited resource.