Meillard comes from the canton of Neuchâtel and learned to ski at the age of two. When she was twelve years old, she and her family moved to the canton of Valais . She started at the Trofeo Topolino in 2014 and won the giant slalom in the U16 category. In November 2014, Meillard began taking part in FIS races at the age of 16 and just two months later celebrated her first victory at this level. Shortly after her debut in the European Cup , she took part in the European Youth Olympic Festival in Malbun in January 2015 , where she finished third in the giant slalom. In February 2015, the Junior Swiss Championship followed in the same discipline.
In the winter of 2015/16 Meillard managed to establish herself with several top 10 rankings in the European Cup, including a second place in Soldeu's slalom in March 2016. Her first appearance in the World Cup was on December 13, 2015 in the slalom in Åre , but didn't finish in the first round. At the 2016 Winter Youth Olympic Games , which took place in Lillehammer in February 2016 , Meillard won the gold medal in giant slalom and the silver medal in combination. A week later, the bronze medal in giant slalom was added at the 2016 Junior World Championships in Sochi .
In her third World Cup appearance, on October 22, 2016 in the giant slalom in Sölden , Meillard placed 18th and thus scored World Cup points for the first time. Three weeks later, she finished in the top 10 when she finished sixth in her fourth Slalom World Cup run by Levi on November 12, 2016 . In February 2017 she won two European Cup slaloms in a row in Bad Wiessee . On January 1, 2018, she finished third at the City Event in Oslo , equivalent to her first podium finish in a World Cup race. Because of her good performance, she was nominated for the Olympic Games in South Korea. There, however, she seriously injured her knee during giant slalom training and then had to end the season. In her first race after the injury at the end of December 2019 in the Lienz slalom , Meillard was eliminated in the 1st round, at the next slalom races in Zagreb and Flachau she could not qualify for the 2nd round.