Kanenaka became the legitimate successor of the family upon the death of his elder brother, Kaneyori HIROHASHI in 1280, then he was successively appointed to Kurodo (Chamberlain) in 1284, and Ushoben (Minor Controller of the Right) in 1287, and Shashoben (Minor Controller of the Left) in 1288, and Uchuben (Middle Controller of the Right) and Sachuben (Middle Controller of the Left) in 1289, and Udaiben (Major Controller of the Right) and Sadaiben (Major Controller of the Left) in the next year with the additional post of Togo no suke, and to Karoo no to (Head Chamberlain) in 1291.
弘安3年（1280年）に兄広橋兼頼が没すると嫡子として扱われ、弘安7年（1284年）に蔵人に任ぜられ、同10年に右少弁、正応元年（1288年）に左少弁、翌年には右中弁、左中弁に、その翌年には右大弁、左大弁に任じられ、春宮亮も兼任、正応4年には蔵人頭に任じられた。