Can a citizen of one EU country vote in local elections in another EU country?

The title basically, but a few points to clarify:

1. Let's call them "EU Country A" and "EU Country B"
2. A citizen of "EU Country A" doesn't yet have a citizenship of "EU Country B".
3. They have decided to get a permanent residency in "EU Country B".

What is the general track to be allowed to vote in "EU Country B" in this case?