Clever Bishop supported by Conservative (6)
I believe the answer is:
bright
'clever' is the definition.
(thesaurus)
'bishop supported by conservative' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'supported by' says to put letters next to each other (letters go below - in down clue).
'conservative' becomes 'right' ('right' can be similar in meaning to 'conservative').
'b'+'right'='BRIGHT'
(Other definitions for bright that I've seen before include "Radiant -- clever" , "Shining; intelligent" , "economist" , "Clever; fine" , "Jolly" .)