On re-evaluation, costlier pet very extravagant (15)

I believe the answer is:

retrospectively

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

'on' is the definition.
Both the definition and answer are adverbs. Maybe they are linked in a way I don't understand?

're-evaluation costlier pet very extravagant' is the wordplay.
'costlier pet very' can be anagrammed to 'RETROSPECTIVELY'.
Though, I am unsure how the anagram is indicated.

Can you help me to learn more?

(Another definition for retrospectively that I've seen is " In a backward-looking manner".)

I've seen this clue in the Sydney Morning Herald.

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