Ill-defined affair that indicates intelligence (4,6)
I believe the answer is:
grey matter
'intelligence' is the definition.
(I've seen this before)
'ill-defined affair' is the wordplay.
'ill-defined' becomes 'grey'.
'affair' becomes 'matter' ('matter' can be a synonym of 'affair').
'grey'+'matter'='GREY MATTER'
'that indicates' is the link.
(Other definitions for grey matter that I've seen before include "Brains" , "stuff in the head" , "Brain tissue" , "intellectual capacity?" , "Issue lacking clear boundaries" .)