Regarding vacating, yes at small airfields it is obvious; you don’t land and stop and sit there, but if ATC is operating then they will at that point issue taxi instructions. I don’t think I have ever been in a situation where they forgot to do that, but I would assume they must either issue these or I “request taxi instructions”.
Interesting and strange to me. There are a few Class D airports in the US that don’t operate dedicated ground control and frequency, or so I understand. I can’t remember being at one, but might have been. Otherwise the protocol is clear: you exit the runway with the entire aircraft past the hold short lines, stop completely, switch frequencies to ground and get taxi clearance to wherever you’re going. Tower is not to required to instruct you to contact Ground because you’re going past the hold short lines (there is nowhere else to go) and then stopping, out of their area of authority. However if it is not too busy they will often say ‘contact Ground’ anyway.
When crossing a parallel or adjacent runway to exit you stay with Tower until getting clear of both runways, between runways is a Tower controlled area, then once past the final set of hold short lines you stop and contact Ground.
@Peter, thanks for clarifying the meaning of apron, I hadn’t heard it before. I’ve also noticed that ground controllers are moving away from ‘ramp’ and now use the word ‘parking’ for reasons unknown to me.
You can’t stop on runway after landing under US rules with an explicit ATC clearance to do so, so naturally you would vacate or go-around if you hear nothing 
