You don't need a licence for private tutoring but you do need credibility, which is why in a lot of fields like science or economics a degree is usually expected for a tutor.
In stuff like art where someone who is rigorously self-tought can be better than someone with an art degree, credibility will be based on your portfolio, capacity to talk to students in ways they understand, and general success as an artist and writer (awards, professional recognitions, affiliation with artist guilds, if you can make a living off of your art already, if you've previously had success being employed for a traditionnally published comic, etc...).