The most common and most likely answer to this crossword clue is the 10 letter word DEFINITIVE
I've seen this crossword clue in The Times
D
E
F
I
N
I
T
I
V
E
More clues leading to the result DEFINITIVE
Buddy explains!

The straight part
We know that "Conclusive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conclusive = definitive.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 DEFINITIVE mean?
DEFINITIVE noun- (grammar) a word, such as a definite article or demonstrative pronoun, that defines or limits something
- An ordinary postage stamp that is part of a series of all denominations or is reprinted as needed to meet demand
- Explicitly defined
- Conclusive or decisive
- Definite, authoritative and complete
- Limiting; determining
- General, not issued for commemorative purposes
- Determined; resolved.