Anyway, even the most gadabout socialite can't be! (2,3,6)

I believe the answer is:

at all events

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'anyway' is the definition.
(I've seen this before)

I can't explain the rest of the clue.

(Other definitions for at all events that I've seen before include "In which Olympic medals may be won" , "Anyway" , "An extremely keen athletics fan may be" , "Whatever happens" , "in the manner of a well-placed deb, say" .)

I've seen this clue in the Evening Standard.

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