When Shiro and Keith of Team Voltron came to see the Blade of Marmora, Kolivan was initially wary of the pair, as the secret organization was not trusting of outsiders. Almost immediately upon the Paladins' arrival, he saw that Keith possessed one of the Marmorite's luxite blades, which pretty much dissolved the little trust he had for them. Kolivan demanded that Keith relinquish the knife and leave the base. But the Red Paladin, hotheaded as always, refused to give it up and insisted on getting answers about his past. Kolivan relented, and allowed Keith to take the Trials of Marmora until he came to knowledge or death.
Kolivan pushed the young man close to breaking point both physically and mentally, despite Shiro's protests, to the point that the Red Lion finally stepped in to save Keith. But at last Keith managed to awaken his knife, which convinced Kolivan to see Allura and formulate a plan to take down Zarkon. Kolivan and the Blade of Marmora are now allies of Team Voltron.
Kolivan, like his society, is highly secretive and bordering on paranoid. He takes a long time to trust strangers outside his group of rebels, as shown by his initial unwillingness to cooperate with Shiro and Keith. But over time he has begun to trust outsiders, allowing Keith to join Blade missions and working with other rebel forces against the Galra Empire.
He remains calm under pressure and rarely loses his composure.
However, he does harbor a great deal of patience and good faith in his subordinates. In his interactions with the human/Galra hybrid, Keith, he borders on being a mentor, constantly reminding the young blade to temper his emotions in order to maintain objectivity over his feelings first and foremost.
Much like his fellow Blades, Kolivan is highly skilled in combat, both with and without his signature weapon, which resembles a sword. Aside from this, he's shown to be an excellent leader and tactician.