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

I believe the answer is:

generical

I'm a little stuck... Click here to teach me more about this clue!

'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 anagramming the letters.
'at last' indicates one should take the final letters.
The final letter of 'hall' is 'l'.
'carnegie' with letters rearranged gives 'generica'.
'generica'+'l'='GENERICAL'

'that's' is the link.

Can you help me to learn more?

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.