Yuuichi Ootori is Kyoya's older brother. He's only seen in the Anime during flashbacks when there's a close up of the family portrait, and is showed sometimes in the Manga. Yuuichi has already graduated at Medical School and works with his father at the same hospital, and as Kyoya defines in the anime, he is the natural heir of Ootori's companies, because he is the eldest son of family.
(Source: Ouran Wikia)