Kavar can generally be characterized as a compassionate Jedi, who is also a skilled warrior. Before Revan made a name for himself in the Mandalorian Wars, the Mandalorians came to see Kavar as a worthy opponent among the Jedi--Fully believing he would be leading the Republic war effort. He involved himself in a few skirmishes with the Mandalorians though generally refrained from joining the war fully, alongside most of the Jedi.
He is one of the 5 Jedi Masters on the Jedi High Council on Coruscant, who oversaw your trial and sentenced you into exile from the order. It was Kavar's idea that exile would be the most appropriate punishment, as he believed it might help them discover what had "happened" to the Exile during the war and how this "Wound" she carries might be healed. This was largely the motivator for their decision and not because of her decision to follow Revan and Malak to war.