I think the punishment will be: to be a tutor to prince Oscar. Teach him common sense and/or etiquette, you know? Some people said to be his personal maid but ... to be his teacher would make more sense, and would give her a lot of occasions to be in contact with Kiel and Rael.
Although I guess to be Rael's aide or to help him find Morina would be hilarious. But I think it's a bit too soon... Depends on the pacing of the manga.