The most common and most likely answer to this crossword clue is the 9 letter word INTUITION
I've seen this crossword clue in The Guardian
I
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I
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More clues leading to the result INTUITION
- Sort of knowledge gained from popular lessons
- Suspicion of home schooling
- Feeling for Greenlander with temperature inside home about zero
- Innate talent for getting something from home schooling
- Home schooling that seems right
- Travel company into changing following popular feeling
- Sixth sense needed in schooling
- Instinctive belief in teaching
- A way to understand things during class
- An unjustified belief in learning
Buddy explains!

The straight part
We know that "Sixth sense" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sixth sense = intuition.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 INTUITION mean?
INTUITION noun- Immediate cognition without the use of conscious rational processes.
- A perceptive insight gained by the use of this faculty.