Magkeev was born in Vladikavkaz and was interested in martial arts as a child, namely taekwondo. Stas switched to football when he was seven years old. At the age of 15, Magkeev got into the Lokomotiv Academy and played for a long time as a defensive midfielder. However, after moving to the youth team, he changed his position and became a central defender. Initially Magkeev played as central defender for Kazanka, but soon he returned to the central defensive midfielder position.

Stanislav made his debut for the main team on May 26, 2019 in the match against Ufa. In 2019 he won the Russian Cup and the Super Cup. In 2020, he was nominated for the Top Five award, which is annually given to the best young footballer of the Russian Premier League.