He was invited to skate in the gala at the 2013 World Team Trophy as the Japanese national novice champion in the same season.

Yamamoto debuted on the ISU Junior Grand Prix series in 2013–14 season, placing 11th in Riga, Latvia, his sole assignment.

At the 2015 World Junior Championships, Yamamoto placed 7th in the short program and 3rd in the free skate to win the bronze medal in his first appearance at that competition.

In February 2016, Yamamoto won the gold medal in the men's singles discipline at the Winter Youth Olympics ahead of Latvia's Deniss Vasiljevs and Russia's Dmitri Aliev.

[3] After missing the entirety of the 2016–2017 season, Yamamoto returned to competition domestically at the 2017–18 Japan Championships, placing ninth.

Again beginning the season with two Challenger assignments, Yamamoto won the silver medal at the 2019 CS U.S. Classic after placing third in the short program and second in the free skate.

the season at the 2019 CS Finlandia Trophy, and led the field after the short program, in which he set a new personal best and landed two quad jumps.

He was overtaken in the free skate by Frenchman Adam Siao Him Fa, but still scored a new personal best in that segment and won the silver medal, his first Grand Prix podium placement.

"[11] At his second event, the 2022 NHK Trophy on home ice in Sapporo, Yamamoto again finished first in the short program with a new personal best score of 96.49, ahead of reigning World champion Shoma Uno.

Winning the silver medal, he said he was pleased to have delivered a satisfactory free skate for the first time in the season and to have achieved his goal of making the podium.

[21] Named to the Japanese team for the 2023 Winter World University Games in Lake Placid, Yamamoto won the gold medal, finishing more than thirty points ahead of silver medalist Tatsuya Tsuboi.

First in the short program despite an underrotated quad jump and a spin error, he was only third in the free skate, but remained in first place overall to claim his first Grand Prix gold medal.

[26] At the 2023–24 Japan Championships, Yamamoto finished second in the short program, albeit more than ten points behind segment leader Shoma Uno.

[27] In the free skate he came third, and placed third overall, winning the bronze medal and standing on the Japanese national podium for the first time in his senior career.