My Klebust started internationally for the first time at the Nordic Junior World Ski Championships in 1986 in Lake Placid and won the gold medal there with the relay. She ran her first of four individual World Cup races in March 1986 in Lahti , which she finished classically in seventh place over 5 km. In addition, she was there second with the relay and reached 29th place in the overall World Cup at the end of the season. In the 1992/93 season she achieved 25th place over 10 km freestyle in Cogne and 53rd place over 5 km classic in Lillehammer and thus reached 61st place in the overall World Cup. In December 1992 she won the Continental Cup in Davos over 5 km classic and took second place there over 5 km freestyle. She completed her last individual World Cup race in February 1995 in Oslo , which she finished classically in 41st place over 30 km.