Intelligent but big-headed? Correct (6)

I believe the answer is:

bright

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'intelligent' is the definition.
(similar in meaning)

'big-headed? correct' is the wordplay.
'big-headed?' becomes 'b' (this could be a standard abbreviation which I don't know about).
'correct' becomes 'right' (right can mean correct).
'b'+'right'='BRIGHT'

'but' is the link.

Can you help me to learn more?

(Other definitions for bright that I've seen before include "Clear" , "Clever - shining - sunny" , "Intelligent; well-lit" , "Vivid; cheerfully lively" , "Illuminated" .)

I've seen this clue in The Irish Independent.

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