Do Tai Chi Trainers need a Permit / Licence to teach / practice Tai Chi in public Chinese parks?

You will want to check with your city and county ordinances to find that out. Different places have different requirements. Typically, you have to have a license in order to conduct a business in a public setting, or you have to be a member of the parks department. For example, I work for a parks and rec department that provides outdoor classes, and anyone who teaches outdoors is an employee of that parks and rec. I couldn't randomly go onto their land and start charging $ to teach.