1. to rise, to emerge (Rare in this sense. The main context I can think of is "smoke" or other kinds of clouds. And in a figurative sense of emotions and feelings that slowly rise, like fatigue, for example. The noun "der Aufstieg" also works for empires and more.)
Opposite (closest): absteigen
2. to be promoted (In a hierarchy. The focus here is on the gradual rise, not the moment of getting one promotion.)
3. to “go up” one series (Used in context of sports leagues, when a team gets to go up one series at the end of a year.)
Opposite (closest): absteigen