The most common and most likely answer to this crossword clue is the 9 letter word ASSERTION
I've seen this crossword clue in The Guardian
A
S
S
E
R
T
I
O
N
More clues leading to the result ASSERTION
- Drunken sots are in contention
- Claim first son has trouble in store
- Such a declaration is treason, in a way
- No one with hair on end underwrites a claim
- Claim Trump’s behind replacing former partner in industry
- Tries somehow to interrupt a member of the family making pronouncement
- Statement in the article about a braid held up with a triumphant cry
- Confident statement and reason it’s wrong
- Distressed señoritas making statement
- Senorita's unusual profession
Buddy explains!

The straight part
We know that "claim" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case claim = assertion.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 ASSERTION mean?
ASSERTION noun- The act of asserting; positive declaration or averment.
- Something which is asserted; a declaration; a statement asserted.
- A statement or declaration which lacks support or evidence.
- Maintenance; vindication
- A statement in a program asserting a condition expected to be true at a particular point, used in debugging.