He is the first Russian in history who won an individual ski jumping World Cup event for men.

At the 2022 Olympics, he was part of the mixed team which won the silver medal.

He won two medals in ski jumping at the 2015 Winter Universiade in Osrblie, Slovakia.

Klimov won the 2018 FIS Ski Jumping Grand Prix.

He then won his first World Cup event in Wisła, becoming the first Russian to achieve that feat.