Kostiukovich and her new partner, Aleksei Briukhanov, made their debut in Moscow at the second stage of the domestic Russian Cup series, the qualifying competition series to the 2021 senior and junior Russian Championships. They placed fourth at the 2021 Russian Junior Championships. In April, Kostiukovich and Briukhanov parted ways with their longtime coaches Ludmila Velikova, Nikolai Velikov, and Vasili Velkikov to move to the camp of Vladislav Zhovnirski and Arina Ushakova in Moscow.