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.