Crossword Genius

Not an officer's training establishment apparently (7,6)

Ross

I believe the answer is:

private school

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

'not an officer's training' is the definition.
I can't tell whether this definition defines the answer.

'establishment apparently' is the wordplay.
I cannot really understand how this works, but
'establishment' could be 'school' (school is a kind of establishment) and 'school' is located in the answer.
The remaining letters 'private' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Globe and Mail.
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