Second is added to improvised encore again (4,4)

I believe the answer is:

once more

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'again' is the definition.
(synonyms)

'second is added to improvised encore' is the wordplay.
I cannot really see how this works, but
'second' could be 're' (prefix meaning second in eg review, re-education) and 're' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Another definition for once more that I've seen is " Again".)

I've seen this clue in The Irish Times.

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