Orica–GreenEDGE (2015–17) In June 2014, World Tour team signed Cort for three years, starting from the 2015 season. where he won stages 18 and 21.
Astana (2018–19) Cort rode for in 2018. On 22 July 2018, Cort won stage 15 of the race after being in a breakaway for most of the day. Cort attacked with to go, and ended up in a breakaway together with
Bauke Mollema and
Ion Izagirre, where he was the fastest man in the final sprint and won the first Tour de France stage of his career.
EF Education First (2020-2023) In August 2019, it was announced that Cort would be joining the team on a two-year contract, from the 2020 season. He won the intermediate stage 6, where he just edged overall race leader
Primož Roglič for the win. On stage 11 he dropped the surviving breakaway riders and was within less than 300 meters from his second stage win, but he was caught by Roglič,
Enric Mas and other riders fighting for the general classification. The very next day Cort survived the two climbs and won his second stage of the Vuelta, crediting his team with setting him up perfectly for the sprint finish. On stage 19 Cort once again found himself at the front of the race near the end of the stage. With less than a kilometer to go his teammate
Lawson Craddock rode at the front of the group to control the pace and put Cort in position to time his attack perfectly, which he then did defeating
Rui Oliveira and
Quinn Simmons in the sprint. Craddock came across the line five seconds later with his arms in the air celebrating the victory of his teammate. At the start of the
2022 Tour de France he took every available mountain point, over the small hills of
Denmark, to earn the polka dot jersey early in the race.{{cite web|url=https://www.cyclingnews.com/news/cort-propelled-toward-polka-dots-as-home-tour-de-france-crowds-scream-his-name/ ==Major results==