Crossword Genius

Principal problem is to crush rise of alien resistance (4,7)

Ross

I believe the answer is:

head teacher

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'principal' is the definition.
('head teacher' can be a synonym of 'principal')

I can't explain the remainder of the clue.

Can you help me to learn more?

(Another definition for head teacher that I've seen is " School principal".)

I've seen this clue in The Telegraph.
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