Extremely smart just wearing cap (9)

I believe the answer is:

brightest

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'extremely smart' is the definition.
Although both the answer and 'smart' are adjectives, they are not in the same form of the adjective.

'just wearing cap' is the wordplay.
'just' becomes 'right' (similar in meaning).
'wearing' is an insertion indicator.
'cap' becomes 'best' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'right' going inside 'best' is 'BRIGHTEST'.

Can you help me to learn more?

(Another definition for brightest that I've seen is " Most intelligent".)

I've seen this clue in The Independent.

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