As the Men in Black animated series takes off from the end of the first film, but skips the plot after Dr. Weaver destroys the Bug, Agent K remains as Agent J's partner while Dr. Weaver has joined the MIB as a medical doctor at the MIB Headquarters.
It is revealed early on in the series that a man known as Alpha was the founding Chief of MIB, and K's mentor, but later turned criminal.
[1] In the second film, at a post office in Truro, Massachusetts, Kevin Brown is recruited by Agent J, to recover the 'Light of Zartha'.
When J arrives from the future to kill Boris at Coney Island, K arrests J and takes him to MIB headquarters, where J reveals his mission.
Thereafter the precognitive alien 'Griffin the Arcanian' guides J and K to Cape Canaveral, Florida, where Col. Edwards helps them launch the ArcNet kill the future Boris but Col. Edwards dies in the process; whereupon K kills the past Boris to erase his future-self's actions.