Intuition is thing that's mysterious (7)
I believe the answer is:
insight
'intuition' is the definition.
(I know that insight is a type of intuition)
'is thing that's mysterious' is the wordplay.
'that's mysterious' is an anagram indicator.
'is'+'thing'='isthing'
'isthing' is an anagram of 'INSIGHT'.
(Other definitions for insight that I've seen before include "Ability to understand" , "Enlightenment" , "Special knowledge" , "apprehension" , "Awareness" .)