Intelligence shown by bishop with correct cape (10)
I believe the answer is:
brightness
'intelligence' is the definition.
(brightness is a kind of intelligence)
'bishop with correct cape' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'with' is a charade indicator (letters next to each other).
'correct' becomes 'right' ('right' can be a synonym of 'correct').
'cape' becomes 'ness' ('ness' can be a synonym of 'cape').
'b'+'right'+'ness'='BRIGHTNESS'
'shown by' is the link.
(Other definitions for brightness that I've seen before include "Luminosity" , "Intelligence" .)