In 1984 she won the bronze medal in the 500 m event.
In the 1000 m competition she finished 37th.
Four years later she finished ninth in the 500 m contest and 20th in the 1000 m event.Her first international competitions were the 1982 European Championships where she won three bronze medals (all-around, 1,000 m and 1,500 m) and a silver medal in the 500 m.
Next year she won a silver and a gold medal in the 500 m at the European and World All-around Championships, respectively, and finished eights overall.
At the 1984 World Championships she again won silver in the 500 m.
During her career, Glebova won six national titles: all-around in 1983, sprint all-around in 1984, 1,000 m in 1982 and 1984, 3,000 m in 1983, and 5,000 m in 1983.
She retired after the 1988 Olympics.
Personal bests:
500 m – 40.39 (1983)
1000 m – 1:22.22 (1984)
1500 m – 2:09.36 (1982)
3000 m – 4:37.97 (1983)
5000 m – 8:07.20 (1983)