Arkham Knight remains the conclusion to the series.
The Batman: Arkham series ended on a (more or less) high note with Batman: Arkham Knight back in 2015; since then, there have been leaks and rumors pointing to the existence of a fifth game in the franchise, albeit following a different continuity.
However, if Kevin Conroy, famed voice actor of Batman (and not just in the games, but across the animated series, movies, and more) is to be believed, there will be no new Batman: Arkham game. Speaking at Comic Con, Konroy said, “You know, I can’t believe that they’re not gonna do another one, but they’re not. Isn’t that amazing? They made literally billions of dollars on those games, but uh no, there’s no plan to do another one. Sorry.”
This seems to rather conclusively rule out the possibility of a new Batman: Arkham game- that said, that doesn’t mean that there won’t be a new Batman game in that vein, period. In fact, it is entirely possible that a new Batman game is developed by Warner Bros., but just that it is not branded Batman: Arkham.
I am sure that many want a new Batman game (beyond just the Telltale ones, I mean)- so hopefully, that is something that ends up happening.