The most common and most likely answer to this crossword clue is the 9 letter word RELIGIOUS
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Buddy explains!

The straight part
We know that "based on belief" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case based on belief = religious.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 RELIGIOUS mean?
RELIGIOUS noun- A member of a religious order, i.e. a monk or nun.
- Concerning religion.
- Committed to the practice or adherence of religion.
- Highly dedicated, as one would be to a religion.