Crossword Genius

Say one should open sort of institution (10)

Ross

I believe the answer is:

collegiate

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

'open sort of institution' is the definition.
Although both the answer and definition are adjectives, I can't understand how they can define each other.

'say one should' is the wordplay.
I cannot really see how this works, but
'say' could be 'eg' (short for 'exempli gratia', 'for example' in Latin) and 'eg' is located in the answer.
'one' could be 'li' (I've seen this in other clues) and 'li' is present in the leftover letters.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for collegiate that I've seen before include "Relating to a particular group of students" , "educational establishment" , "in institution" , "Constituted like Oxford or Cambridge universities" .)

I've seen this clue in The Sunday Times.
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