Goes swiftly up for a violin (5)

I believe the answer is:

strad

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'for a violin' is the definition.
(Stradivari abbreviation)

I don't understand how the rest of the clue works.

(Other definitions for strad that I've seen before include "Old, very expensive violin (abbr)" , "Noted violin" , "musical instrument" , "Top-quality violin (abbr.)" , "that Grappelli could have played" .)

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

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