Klimková, who started for the CH Štrbské Pleso, ran in March 1979 in Štrbské Pleso over 20 km for the first time in the unofficial cross-country skiing world cup and took seventh place. In February 1984 she took part in the Winter Olympics in Sarajevo . She achieved the 24th place over 20 km. The following year she was tenth over 20 km, ninth over 10 km and sixth over 5 km at the World Championships in Seefeld in Tirol . In addition, she ran there together with Dagmar Švubová , Alžbeta Havrančíková and Gabriela Svobodová in fifth place in the season. In February 1985 she reached in Nové Město with third place over 5 km, her only podium finish in the individual World Cup and at the end of the season 1984/85 with 17th place in the overall World Cup, her best overall result. In December 1986 she won second place with the relay in Cogne . At the 1987 World Championships in Oberstdorf , she finished 18th over 10 km classic and ninth place with the relay. In her last active season she came at the 1988 Winter Olympics in Calgary on 35th place over 10 km classic, 22nd place over 5 km classic and 17th place over 20 km freestyle. In addition, she won there together with Ľubomíra Balážová , Ivana Rádlová and Alžběta Havrančíková seventh place in the season.
At the Czechoslovak Championships Klimková won twice over 10 km (1985, 1987) and with the relay of CH Štrbské Pleso (1985, 1988) and once over 20 km (1987).
Participation in World Championships and Olympic Winter Games
Czechoslovakia