Sixth sense during lessons (9)
I believe the answer is:
intuition
'sixth sense' is the definition.
(both can mean an unconscious instinct)
'during lessons' is the wordplay.
'during' becomes 'in' (e.g. during February means in February).
'lessons' becomes 'tuition' (I've seen this before).
'in'+'tuition'='INTUITION'
(Other definitions for intuition that I've seen before include "an instinctive thing" , "Unjustified belief" , "Gut feeling" , "Perception" , "Instinct" .)