Your usage is actually correct. Which is great, considering many native English speakers get this one wrong. The heuristic we hear in school is something like "use 'affect' as a verb and 'effect' as a noun," which like many grammar heuristics is of course an oversimplification of reality. Usage of effect as a verb isn't super common in general conversation by native English speakers whereas I think most might choose to say something like "establish authority" instead in this case, but still your intention is still clear.
affect
effect
Effect is correct here.
Because the other comment didn't spell it out: effect is correct there. Effect as a verb means something like "to cause to happen". Don't pretend effect/affect is just a noun/verb split. Both words have meanings as both verbs and nouns. It's best to just learn both meanings of each instead of following some rule that's wrong a fair amount of time.