Just to clear everything up, let me give a little backstory.
Sam convinced Dean to attend university after he got accepted into Harvard his senior year of high school. With the help of his uncle Bobby’s friend, Missouri Moseley, the dean of Kripke University, Dean was able to attend school an hour from Harvard.
This is the very school Castiel Novak attends as a fourth year student with his roommate Ash. Dean and Castiel aren’t friends - yet. They talk when it is required of them but other than Ash, they have nothing in common. But having Ash in common means they are around each other often.
The only characters that attend university somewhere other than Kripke U are Sam, Jess, and the Ruby’s.
When you ask about new characters, they’re introduced.
Professors: Michael, Lucifer(Harvard), Zachariah, Uriel, Alastair, Azael(Harvard), Lilith(Harvard), Eve, Raphael.