Society girl runs — smooth mover? (6)

I believe the answer is:

skater

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'smooth mover?' is the definition.
The answer and definition can be both people as well as being singular nouns.
Maybe you can see a link between them that I can't see?

'society girl runs' is the wordplay.
'society' becomes 's' (common abbreviation in names of organisations).
'girl' becomes 'kate' (girl's name).
'runs' becomes 'r' (cricket abbreviation).
's'+'kate'+'r'='SKATER'

Can you help me to learn more?

(Other definitions for skater that I've seen before include "Dean, perhaps" , "Mover across ice" , "one should go on ice" , "Glider on ice" , "Rink glider" .)

I've seen this clue in The Independent.

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