The school play? (5)

I believe the answer is:

rugby

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This clue could be a double definition.

'the school' is the first definition.
(English private school)

'play?' is the second definition.
The definition and answer can be both acts as well as being singular nouns.
Perhaps you can see an association between them that I don't see?

Can you help me to learn more?

(Other definitions for rugby that I've seen before include "Public school - sport" , "Game with oval ball" , "Public school founded in 1567" , "Team sport" , "Type of football; school" .)

I've seen this clue in the Evening Standard.

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