Watched the Captain Marvel movie recently. Got this doubt after seeing it.
What is the relation between Mar-Vell and Yon-Rogg?
Not much context is given about this in the movies, so this answer mostly draws from the comics. While the specifics probably differ, the general tone of their relationship seem to be the same.
Mar-Vell was a spy who secretly defected from the Kree empire, while Yon-Rogg was a soldier in the Kree Imperial Army who stayed loyal. They had been on several missions together before, and on several of them Mar-Vell impressed their superiors. Mar-Vell was also the target of a chrush from another Kree named Una, making Yon-Rogg jealous. Even before the defection, Yon-Rogg was jealous of his* success and accomplishments and tried to have him killed. After the betrayal was uncovered, Yon-Rogg was part of the mission to hunt him down and execute him, and was happy to do so.
*Mar-Vell is male in the comics