The most common and most likely answer to this crossword clue is the 10 letter word PHILOSOPHY
I've seen this crossword clue in The Guardian
P
H
I
L
O
S
O
P
H
Y
More clues leading to the result PHILOSOPHY
- Weird hippy school’s not about discipline
- Outlook extremely healthy after botched Polish surgery
- Prince editing his holy work in pursuit of wisdom
- School with hippy founders ditching conservative belief system
- System of belief in operation aboard holy ship at sea
- Jewish thinker, terribly posh, with yen for academic discipline
- Conservative abandons school with hippy, radical way of thinking
- Thinking of Socrates?
- System of belief nastily put as ‘popish’ and ‘holy’
- Ideology from Berlin?
Buddy explains!

The straight part
We know that "belief system" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case belief system = philosophy.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 PHILOSOPHY mean?
PHILOSOPHY noun- The love of wisdom.
- An academic discipline that seeks truth through reasoning rather than empiricism.
- A comprehensive system of belief.
- A view or outlook regarding fundamental principles underlying some domain.
- A general principle (usually moral).
- A broader branch of (non-applied) science.
- A calm and thoughtful demeanor; calmness of temper.
- To philosophize.
- The size of type between long primer and pica, standardized as 11 point.