Glebowa first appeared internationally in 1982. At the all-around European championship in Heerenveen , she won bronze in the all-around event, after finishing second over 500 meters and third over 1000 and 1500 meters. She also competed in the all-around European and World Championships in 1983 and was second or first over 500 meters, but was only eighth overall due to poor performance over the long distances. The following year Glebowa took part in the Winter Olympics in Sarajevo . She was able to win the bronze medal over 500 meters. She finished the race over 1000 meters after a fall in 37th place. In the same year she also won bronze at the Sprint World Championships in Trondheim . In 1988 Glebowa took part in the Winter Olympics for the second time . In Calgary she was ninth in the 500 meters and 20th in the 1,000 meters. She then ended her active career.