Go to the empty classroom and teach a class.
You need to raise the education level to then increase the authority.
(You can check education and authority in the office)
To make your life easier you could also buy the textbooks upgrade for the college, so your classes are more effective.
Also you might find a book in the college library to help you teach, maybe ask Madison for advice?
But the education level drops a bit each week.
You could ask Veronica for advice on that, or if you know the merchant in the field you can buy a... potted crystal...
Magic stuff, don't ask questions you don't want the answers.