Saints Row The Third is coming to PlayStation 4 next month by way of a remaster, but that doesn't mean the series' next instalment has been put on hold. As previously reported, Saints Row 5 (or whatever it ends up being called) is happening, and the official Twitter account has reiterated that, yes, the game is still in development.
As far as we know, the title is still set to be revealed in 2020, although given the coronavirus situation, we wouldn't bank on everything going exactly as planned. Hopefully we hear more soon.
Meanwhile, Saints Row The Third Remastered is actually being developed by Sperasoft, not usual Saints Row developer Volition. We can assume Volition is all-in on Saints Row 5 at this point.