Tamara Press competed for VSS Trud. Together with her younger sister, Irina Press, who was also a track athlete, she was half of the "Press Sisters", a duo who won almost everything that there was to win in track and field, except for distance running.
Tamara was also successful in the European championships. In 1958 in Stockholm she was third in the shot put, and in 1962 in Belgrade she was the European champion in the shot put as well as the discus.
Both sisters were accused of actually being men. Others thought that they might be hermaphrodites, or that they were being injected with male hormones in order to make them stronger. Detractors called them the "Press Brothers". However, both sisters had left the sporting scene by the time that gender verification for all international sporting female events was made mandatory in 1966 (curtailed in Sydney in 2000).