Bishop, correct and smart (6)
I believe the answer is:
'smart' is the definition.
'bishop correct' is the wordplay.
'bishop' becomes 'B' (abbreviation used in chess).
'correct' becomes 'right' (synonyms).
'and' acts as a link.
(Other definitions for bright that I've seen before include "Illuminated" , "Effulgent" , "Jolly" , "Clever; vivid" , "Clear" .)