[12] Kaya won a silver medal in the all-around behind Ukraine's Oleg Verniaiev at the 2017 Stuttgart World Cup.

[13] Then at the Szombathely World Challenge Cup, he won gold medals on the pommel horse and parallel bars.

[15] He was then selected to compete at the World Championships in Doha alongside Kenzō Shirai, Yusuke Tanaka, Wataru Tanigawa, and Kōhei Uchimura.

[19][20] Kaya won a bronze medal in the all-around at the Birmingham World Cup behind Nikita Nagornyy and Sun Wei.

[21] He was then selected to represent Japan at the 2019 Summer Universiade, winning the team gold medal alongside brothers Wataru and Kakeru Tanigawa.

[24][25] Kaya then competed at the World Championships alongside the Tanigawa brothers, Daiki Hashimoto, and Yuya Kamoto, and they won the bronze medal behind Russia and China.

They won the silver medal in the team final, finishing only 0.103 behind the gold medal-winning Russian Olympic Committee.

[4] Individually, Kaya qualified for the pommel horse final and won the bronze medal behind Max Whitlock and Lee Chih-kai.

[37] At the 2021 World Championships held in Kitakyushu, Kaya won the silver on the pommel horse,[38] and he placed sixth on both the floor exercise and parallel bars.

[44] He was selected to compete at the World Championships alongside Kenta Chiba, Daiki Hashimoto, Kazuki Minami, and Kaito Sugimoto.

[49] After the World Championships, he once again competed at the Swiss Cup Zürich with Chiaki Hatakeda, and they won the silver medal behind the American team.

[50] Kaya finished second in the all-around at the NHK Trophy and was selected to represent Japan at the 2024 Summer Olympics alongside Daiki Hashimoto, Shinnosuke Oka, Takaaki Sugino, and Wataru Tanigawa.