Applicable to any group that's playing Carnegie Hall at last (9)

I believe the answer is:

generical

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'applicable to any group' is the definition.
I can't judge whether this defines the answer.

'playing carnegie hall at last' is the wordplay.
'playing' indicates an anagram.
'at last' says to take the final letters.
The last letter of 'hall' is 'l'.
'carnegie' is an anagram of 'generica'.
'generica'+'l'='GENERICAL'

'that's' acts as a link.

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I've seen this clue in The Independent.

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