Belief in teaching (9)
I believe the answer is:
intuition
'belief' is the definition.
(intuition is a kind of belief)
'in teaching' is the wordplay.
'teaching' becomes 'tuition' (tuition is a kind of teaching).
'in'+'tuition'='INTUITION'
(Other definitions for intuition that I've seen before include "Hunch" , "Ability to understand immediately" , "Instinct" , "Innate understanding" , "Instinctive knowledge" .)