Sixth sense during education (9)
I believe the answer is:
intuition
'sixth sense' is the definition.
(both can mean an unconscious instinct)
'during education' is the wordplay.
'during' becomes 'in' (e.g. during February means in February).
'education' becomes 'tuition' (tuition is a kind of education).
'in'+'tuition'='INTUITION'
(Other definitions for intuition that I've seen before include "Suspicion" , "Hunch" , "Instinctive knowledge" , "Ability to understand immediately" , "Unjustified belief" .)