First alternates for the 2013 European Championships, Stolbova/Klimov were called up to replace Vera Bazarova / Yuri Larionov who withdrew due to Larionov's wrist injury.After finishing sixth at Europeans in Zagreb, they won their first senior international title at the 2013 Bavarian Open.Stolbova/Klimov decided not to compete at the 2015 World Championships in Shanghai, China, as they wanted to focus on learning new throw jumps.Stolbova/Klimov started the 2015–16 season competing in a challenger series at the 2015 Ondrej Nepela Trophy where they won the gold medal.
At the 2016 World Championships in Boston, the pair placed 5th in the short program, 4th in the free skate, and 4th overall.
They also debuted on the senior GP circuit, finishing 5th at Skate America. At the 2011 Russian Championships, Stolbova/Klimov finished sixth overall in their senior national debut and won their second junior national title.
They were the silver medalists at the 2011 World Junior Championships.
In the 2014–15 season, Stolbova/Klimov won both of their Grand Prix events, the 2014 Rostelecom Cup and 2014 Trophee Eric Bompard, and took silver at the Grand Prix Final behind Canada's Meagan Duhamel / Eric Radford.
They won their second consecutive national title at the 2015 Russian Championships and went on to win silver at the 2015 European Championships behind Kavaguti/Smirnov.