Zdeňka Pešatová jumped at the Junior World Championships 2013 in Liberec on the 37th place in the individual and on the 7th place in the team competition. At the start of the 2013/14 Alpine Cup season, she achieved third place in the first competition in Pöhla , and she was able to repeat this result in the third competition on the Ochsenkopfschanze in Bischofsgrün.
On January 18, 2015, Pešatová in Falun made her debut in the Continental Cup . After fifth place in the first competition, she achieved her first podium finish in third in the second competition.
In the 2015/16 season, Pešatová achieved several podium placements in the Alpine Cup. At the competitions on the Pöhlbachschanze she celebrated a double victory. Pešatová was also able to collect World Cup points three times in the World Cup and finished the season in the Ski Jumping World Cup 2015/16 in 42nd place.