Kaja Norbye skied for the first time in her hometown Oslo when she was three years old. At the age of eight, she began to train with her ski club and to emulate her two older sisters.
She competed in her first FIS races in Sweden at the age of 16 and achieved good results straight away. In February 2016, she made her European Cup debut in the Pamporowo slalom . After missing a large part of the 2016/17 season, she returned with good FIS and European Cup results and started at a Junior World Championship in Davos for the first time in February 2018 . In combination and slalom, she achieved top 10 placements with ranks seven and eight. At the end of the season, she won her first national title in slalom. In the coming winter she was able to continuously improve her European Cup results and after two second places she won a giant slalom in Berchtesgaden . At her second Junior World Championship in Fassatall , Norbye won silver in the combined and bronze in the giant slalom. She finished the European Cup season in third place overall and won the giant slalom classification.
In March 2019 she made her World Cup debut in the giant slalom in Špindlerův Mlýn and achieved her first World Cup points with 22nd place. She was able to equalize this result in Courchevel the following December . At the 2020 Junior World Championships in Narvik , she won bronze in the giant slalom.