The two men, codenamed Bai Yaksha and Shura, were ordered to kill the Night King. Gintoki is dying and Takasugi is seriously injured. Kamui became obsessed with Gintoki, who killed the Night King himself, and saved him for some purpose. Dissatisfied with their bond, Kamui tried to change Takasugi's memory and turn the two against each other. But it failed :3
After that comes the revenge story of the two (possibly), with the Shinsengumi appearing in the middle. It's not a too heavy story.