Praise one's former spouse to a pupil (5)

I believe the answer is:

extol

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'praise one's' is the definition.
'extol' can be an answer for 'praise' (extolling is a kind of praising). I am not certain of the 'one's' bit.

'former spouse to a pupil' is the wordplay.
'former spouse' becomes 'ex' (an ex-spouse).
'a pupil' becomes 'L' (as in a learner driver with L-plates on their car).
'ex'+'to'+'l'='EXTOL'

Can you help me to learn more?

(Other definitions for extol that I've seen before include "Exalt" , "Cry up" , "Praise greatly" , "celebrate" , "Say great things about" .)

I've seen this clue in the Evening Standard.

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