There are many brave and noble Kree in the Marvel Cosmic canon. Zarek is not one of them.
Like so many of the blue-skinned Kree, Zarek is an ideologue, espousing an unfortunately racist view over the pink-skinned Kree.
While he was in good standing with the Intelligence Supreme, Zarek served the office of Imperial Minister. Under Zarek's leadership, the Kree engaged in significant conflicts with the Shi'ar and the Brood, but were stymied when the Fantastic Four drove off not only their Intergalactic Sentry but Ronan the Accuser as well.
Forming a conspiracy with Ronan, Zarek schemed to build up Captain Mar-Vell as a hero, then brand him a traitor to create a scandal that would overthrow the Intelligence Supreme. Mar-Vell was assigned to Earth to spy on the human race and obtain revenge on them on behalf of his people, but Mar-Vell came to love Earth's people and eventually accepted Earth as his second home.
When Zarek and Ronan finally enacted their plan, Mar-Vell opposed them, and the Supremor turned out to have been aware of the conspiracy all along.
Ronan and Zarek made desperate plans to assassinate the Intelligence Supreme with an ::anti-matter bomb. Mar-Vell tried to sacrifice himself to save the Supremor but the Kree ruler had already disengaged the bomb. Mar-Vell won acclaim within the Kree Empire while Zarek was sent into exile.
Later, Zarek and other blue-skinned Kree relocated to the Earth's moon where they established the Lunatic Legions (gotta love Steve Englehart's brain post-Starlin), an organization whose goal was to reestablish blue supremacy in the Empire; they intended for all like-minded blue Kree to join them in the BlueCityof the Moon.
The Intelligence Supreme seemingly supported their goals, but only to further his aim of shaping Mar-Vell into a finer warrior. The Supremor believed the defeat of the Lunatic Legion would work toward this goal.
Zarek's continued exile spared him from the near-destruction of the Kree Empire at Shi'ar hands. (Those pesky boids!) He was last seen on the planet Godthob Omega, apparently one of those enthralled by Glorian. Whether he escaped from Godthob when it was besieged by the Annihilation Wave is unknown.