Relating to non-democratic rule, I coach girl to rebel (10)

I believe the answer is:

oligarchic

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

'relating to non-democratic rule' is the definition.
I can't judge whether this defines the answer.

'i coach girl to rebel' is the wordplay.
'to rebel' indicates an anagram.
'i'+'coach'+'girl'='icoachgirl'
'icoachgirl' with letters rearranged gives 'OLIGARCHIC'.

Can you help me to learn more?

(Other definitions for oligarchic that I've seen before include "Relating to rule by a few" , "sort of government" .)

I've seen this clue in The Independent.

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