In the comics, he has a serious grudge against Wolverine given that the mutant killed his father while escaping the original Weapon X program, and given that Logan is set in the future, it’s entirely possible that element of the character could wind up becoming part of the big screen X-Men universe.
In addition to being the son of one of the original Weapon X developers (the program that gave Wolverine his adamantium skeleton), he is the scientist who winds up becoming responsible for the creation of X-23 – a.k.a. the young girl in Logan being played by Dafne Keen.
According to the caption on this Tweet, the great British actor will be playing a character named Rice – and if we use Marvel history and context for clues, it seems that Richard E. Grant will be playing Dr. Zander Rice.