The Kohen Gadol (High Priest), when a relative of his passes away, tears his garment from the bottom, near his feet. It was implied that Elazar and Itamar, his other two sons, who were regular Kohanim (priests), he tears it in the usual manner at the top of his garment near his chest. Were not even allowed to bring the korban (offering). But for the ordinary individual or the ordinary Kohen, when his relative dies...
Another difference between a Kohen Gadol and a regular Kohen, in terms of Avelut, the laws of mourning, is that a Kohen Gadol is somebody whose relative just passed away. The laws of mourning concern how they deal with the stage of Aninut (pre-burial mourning) and an Onen (pre-burial mourner). In the last Mishnah, we said that the Kohen Gadol is... That's until the end of the day that a relative passed away. The difference when it comes to there, a Kohen Gadol is allowed to bring korbanot when he's in that stage of Aninut as an Onen, but he's not allowed to eat the meat of the korbanot at that time. The hedyot (ordinary individual) is not allowed to offer korbanot, and he's not allowed to eat korbanot.
During that stage of Aninut, we learned this from Aharon HaKohen, who was Kohen Gadol. When a relative of theirs dies, they don't grow their hair out, nor do they tear their garments. What we mean by that is that they don't tear their garments in the normal way other people who are mourning would tear them. When his two sons, Nadav and Avihu, passed away, he brought korbanot, the Mishnah says, but he commented that it was not okay for him to eat the meat of that korban.