Your Prestige will increase automatically by buying new rooms, furniture and by upgrading the items you already have on your campus. You can see your prestige indicator in the upper part of the screen (star icon).
The higher your prestige is, the more prestigious teachers would want to work for you. If you tap on the teacher's icon (lower-right side of the screen), you will find a star in their description, indicating their prestige. If they have more prestige than your university, they will ask for a higher wage and vice-versa.
As a rector, you should study each situation and try to balance the prestige and the Knowledge points that a particular teacher offers in his/her description in the chosen academic field (they could have great numbers in Science but horrible stats in Fine Arts, for example).
We recommend you revise your teacher staff regularly and hire new ones according to your growth strategy.