It is very common for developers to plan or at least make an outline for potential sequels when making a game with a high potential for success and impact (even some that don't), and The Last of Us: Part II is no exception.
Neil Druckmann and Halley Gross, the director and narrative lead on Naughty Dog's latest game, was being interviewed on the latest episode of the Script Apart podcast when Druckmann said the following about The Last of Us III/The Last of Us: Part III:
"I don't know how much I want to reveal. Halley and I did write an outline for a story...that we're not making, but I hope one day can see the light of day, that explores a little bit what happens after this game. We'll see."
It's very important to note that this a far from saying that we'll definitely get another The Last of Us game (besides the remake of the first game). Druckmann even says as much by stating that the entire kennel will have to be extremely passionate about projects because they're asked to put so much work, blood, sweat and tears into them for many years. Top that with the fact that Naughty Dog is working on a new IP, and it's clear we won't see a potential The Last of Us 3 for a loooooooong time...if ever.