Two chaps with their own academy? (5)

I believe the answer is:

royal

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'their own academy?' is the definition.
I can't judge whether this definition defines the answer.

'two chaps' is the wordplay.
'two chaps' means two substitutions for 'chap'.
'chap' becomes 'roy' ().
'chap' becomes 'Al' (man's name).
'roy'+'al'='ROYAL'

'with' acts as a link.

Can you help me to learn more?

(Other definitions for royal that I've seen before include "Suitable for king or queen" , "What we may get used for individual" , "one in palace?" , "Queen Mary, for example" , "complete" .)

I've seen this clue in the Evening Standard.

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