New clue I can’t gradually introduce (9)

I believe the answer is:

inculcate

I'm a little stuck... Click here to teach me more about this clue!

'gradually introduce' is the definition.
I can't judge whether this defines the answer.

'new clue i can't' is the wordplay.
'new' is an anagram indicator.
'clue'+'i'+'cant'='clueicant'
'clueicant' with letters rearranged gives 'INCULCATE'.

Can you help me to learn more?

(Other definitions for inculcate that I've seen before include "Instil (idea) by persistent instruction" , "Impress on the mind" , "drill" , "Din into" , "Habitually stress the idea" .)

I've seen this clue in The Times.

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