He becomes an auror and the eventually the head auror. According to JK Rowling in an interview shortly after the release of the last book.
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He is the caretaker.
Basically (If I remember correctly) Hogwarts is a middle/high school and then you go straight from there to a sort of apprenticeship job then you get a job. No college.
Hogwarts exists only in the Harry Potter series.
He left at the end of Harry Potter and the Prisoner of Azkaban.
He spent it at Hogwarts.