Drury began his sports career as an alpine ski racer . From 2005 to 2014, he mainly competed in the Nor-Am Cup and FIS races and won six FIS races. As a ski crosser he started in Val Thorens for the first time in the European Cup in January 2015 and finished 26th and 4th. The following month he won two victories in the Nor-Am-Cup and thus won the ski-cross discipline of the Nor-Am-Cup. After winning the European Cup race in Pitztal at the beginning of the 2015/16 season, he started the Freestyle Skiing World Cup in Montafon for the first time on December 5, 2015 , finishing in 41st place. In the further course of the season he came under the top ten four times and thus finished 17th in the Ski Cross World Cup.
In the following 2016/17 season , Drury achieved eight top ten finishes in 14 World Cup starts and thus came eighth in the Ski Cross World Cup. At the season highlight, the 2017 World Championships in the Sierra Nevada , he finished 27th. After finishing 14th in Val Thorens at the beginning of the 2017/18 season , he achieved his first podium finish in the World Cup with second place in Arosa . At the 2018 Winter Olympics in Pyeongchang , Drury advanced to the final run, fell and took fourth place. On the other hand, he won the bronze medal at the 2019 World Championships in Park City . During the 2019/20 season , Drury was superior to the competition: he won four races and came second three times, which meant he won the discipline standings by a large margin.