The most common and most likely answer to this crossword clue is the 11 letter word PRESUMPTION
I've seen this crossword clue in The Sunday Telegraph
P
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More clues leading to the result PRESUMPTION
Buddy explains!

The straight part
We know that "Unproven belief" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unproven belief = presumption.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 PRESUMPTION mean?
PRESUMPTION noun- The act of presuming, or something presumed
- The belief of something based upon reasonable evidence, or upon something known to be true
- The condition upon which something is presumed
- Arrogant behaviour; the act of venturing beyond due bounds of reverence or respect
- An inference that a trier of fact is either permitted or required to draw under certain factual circumstances (as prescribed by legislative or judicial law) unless the party against whom the inference is drawn is able to rebut it with admissible, competent evidence.