A new Filbert could be a bit of a thinker (4,5)

I believe the answer is:

left brain

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'a bit of a thinker' is the definition.
I can't tell whether this defines the answer.

'a new filbert could be' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'could be' indicates anagramming the letters.
'a'+'n'+'filbert'='anfilbert'
'anfilbert' is an anagram of 'LEFT BRAIN'.

Can you help me to learn more?

(Another definition for left brain that I've seen is " language centre".)

I've seen this clue in The Independent.

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