A piano expert, playing allegro? (5)

I believe the answer is:

apace

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'playing allegro?' is the definition.
Both the answer and definition are adverbs. Perhaps you can see a link between them that I can't see?

'a piano expert' is the wordplay.
'piano' becomes 'p' (musical abbreviation).
'expert' becomes 'ace' (ace can informally mean very good).
'a'+'p'+'ace'='APACE'

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(Other definitions for apace that I've seen before include "fast" , "Quick" , "At a rapid rate" , "Swiftly, quickly" , "flat out" .)

I've seen this clue in The Times.

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