Thanks! It depends on exactly what you're planning, but CodaLab (https://codalab.lisn.upsaclay.fr/competitions/) or their new platform CodaBench (https://www.codabench.org/) will probably work well.

They both allow you to run competitions for free, and people do use them for teaching purposes (you'll see some examples if you browse through the list of competitions).

I'm planning on writing a shorter blog post on running competitions soon.