Instil confidence in wild-born cougar? (9)

I believe the answer is:

encourage

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'instil' is the definition.
Although both the answer and definition are verbs in their base form, I don't see how one could define the other.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for encourage that I've seen before include "Spurs on" , "Egg on" , "Motivate" , "Recommend" , "Cheer" .)

I've seen this clue in the Sydney Morning Herald.

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