Based on the slew of "Logan" trailers, it is evident that this movie will take place far into the future. Around this time, Wolverine has already begun to age and his healing powers are not as efficient as they were before. Another peculiar thing about the third "Wolverine" movie is its timeline in the "X-Men" universe.
Wolverine and Professor X are the only members of X-Men visible in the trailers, which leads to the question of where the other mutants and X-Men team members are. A consistent explanation as to the absence of mutants is that the film is based on the "Old Man Logan" comics series. Wolverine is one of the last surviving mutants. According to ScreenRant, he and the others are in hiding until another superhero comes along and asks for their help. The seemingly dystopian setting is a result of villains coming together and wiping out the heroes.
In the comics, the villains came to the X-Mansion. Wolverine sprang into action to save the children and managed to kill a handful of enemies. However, he later realized that the only villain to visit the X-Mansion that time was Mysterio, and that the latter used his powers to make Wolverine believe that he was fighting villains when in fact he was killing his friends.
It is likely that this same event will be used in "Logan" to explain the absence of the other X-Men members. It would also explain why Wolverine is in hiding and hesitant to use his powers again.
Another possible explanation to the absence of mutants is Essex Corporation. In "X-Men: Apocalypse," Essex Corporation was able to acquire mutant blood samples for the Weapon X project. Interestingly, Essex is also behind the experiments that led to the creation of X-23, which probably means that the company has been doing a lot of experiments on mutantkind since.
Meanwhile, "Logan" has been stirring a lot of buzz ahead of its premiere especially because it is dubbed as Hugh Jackman's last movie as Wolverine. However, there are speculations suggesting that he would still appear in future "X-Men" titles, particularly "Deadpool." According to Metro, Fox has added three minutes to the "Logan" movie runtime. If anything, rumors suggest that the studio may have added a post-credit scene.