A meeting place for the single person (5)

I believe the answer is:

ascot

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'a meeting' is the definition.
(horse racing meeting)

I cannot understand how the remainder of the clue works.

(Other definitions for ascot that I've seen before include "Fungus affecting wood" , "somewhere in Berks" , "sporting venue" , "Town with racecourse" , "Where the Queen often sees racehorses" .)

I've seen this clue in the Evening Standard.

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