Warner Bros. reportedly won't make a new Superman solo movie for a while. The Last Son of Krypton helped usher in the studio's DC Extended Universe just five years ago, but the results were never stellar. Both Man of Steel and Batman v Superman were extremely polarizing due to their depictions of classic superheroes. In Kal-El's case, audiences criticized Zack Snyder for portraying Superman as a brooding, conflicted individual who felt burdened by his responsibility to help others.
The studio attempted to course correct for Justice League, and when Henry Cavill's Superman returned, he was far more in line with the "traditional" portrayal of the character. However, that didn't help much, as Justice League was panned critically and came up well short at the box office. In the aftermath, WB is trying to figure out what their strategy should be moving forward, and apparently it involves putting Clark Kent on the back burner for now.
In the THR report that broke Cavill's departure from the DCEU, it's stated WB probably won't produce another Superman standalone "for at least several years." Currently, their priority is getting the in-development Supergirl film off the ground, and they'll return to Superman at a later date with a new actor in a reboot.
It's unfortunate contract negotiations fell apart with Cavill, especially since the actor was interested in starring in the long-rumored Man of Steel 2. However, it's probably for the best WB isn't going to rush another new Superman onscreen. During the Golden Age of superhero films in the 21st century, the character has proven to be a tricky sell for general audiences. 2006's Superman Returns (with Brandon Routh) wasn't successful enough to warrant a followup, and then Cavill's interpretation struggled to connect. This decision also plays into the studio's desire to "reset" the franchise as they focus on the bevy of other DC Comics characters they have at their disposal. Wonder Woman is clearly the face of the series now, and they have other titles like Shazam and Aquaman in the pipeline.
It'll be interesting to see when WB decides to revisit Superman on the big screen. There's no denying this remains a popular and recognizable IP, so the character likely won't be gone from the movies forever. However, the filmmakers are going to have to work hard at finding an approach that'll land with viewers, so the latest attempt is more successful than the previous two. Superman has such a rich history and mythology, he should be able to carry his own trilogy - like so many other comic book characters have. Hopefully the next time we see Kal-El, WB has figured it out.