Dull affair that shows intelligence (4,6)
I believe the answer is:
grey matter
'intelligence' is the definition.
(I've seen this before)
'dull affair' is the wordplay.
'dull' becomes 'grey' (I've seen this before).
'affair' becomes 'matter' ('matter' can be a synonym of 'affair').
'grey'+'matter'='GREY MATTER'
'that shows' is the link.
(Other definitions for grey matter that I've seen before include "Brain tissue" , "Brains" , "stuff in the head" , "Intelligence; the brain" , "intellectual capacity?" .)