Very keen to be concealed by a pedagogue (4)

I believe the answer is:

agog

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'very keen' is the definition.
'agog' can be an answer for 'keen' (I've seen this in another clue). I'm not certain of the 'very' bit.

'concealed by a pedagogue' is the wordplay.
'concealed by' says the answer is hidden in the clue.
'AGOG' is hidden in the letters of 'pedagogue'.

'to be' acts as a link.

Can you help me to learn more?

(Other definitions for agog that I've seen before include "Eager or curious" , "Enthralled" , "All ears" , "Perfect" , "Very eager (to hear/see)" .)

I've seen this clue in the Evening Standard.

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