then there's some chaos, but there's a lot of behind-the-scenes work being done even at the time of Return of the Jedi. The New Republic becomes what the Old Republic was and also (if you keep reading) degenerates into what the Old Republic became. although not immediately, for a time there's a lot of "improvement", but it still degenerates into bureaucracy. But the initial transition is (relatively) stable. Remember, the Empire was not around that long. It would be relatively simple for all the planets that were members of the Galactic Republic to resume business as usual.

The Empire on its own is--of course--questionably stable. It relies on the might of the Emperor and a measure of consistency from the post, not to mention a matter of efficiency all around. And just like we saw in Roman history, once that errodes... We never really get the opportunity to see how long and stable the Empire would last and even Sith Lords die.