Green began learning to skate when she was five years old. She teamed up with her brother in August 2009 and joined the Wheaton Ice Skating Academy in September. The siblings took gold in the juvenile category at the 2013 U.S. Championships and won the intermediate title at the 2014 edition. At the 2015 and 2016 U.S. Championships, the Greens took gold in the novice category. They then moved up to the junior level domestically and placed fifth at the 2017 U.S. Championships.
2017–18 season: International junior debut
Having become age-eligible for junior international events, the Greens made their ISU Junior Grand Prix debut, winning bronze in Riga, Latvia, and Gdańsk, Poland. They finished as third alternates for the JGP Final. In January, they took silver at the 2018 U.S. Championships, scoring 12.46 points less than champions Christina Carreira / Anthony Ponomarenko, and were assigned to the 2018 World Junior Championships in Sofia. In Bulgaria, the siblings ranked fifth in the short dance, seventh in the free dance, and sixth overall.
2018–19 season: National junior championship
The Greens withdrew from their JGP assignments due to Caroline's illness. She subsequently commented that having been off the ice for two months and having to readjust to skating was a significant challenge, as neither sibling had had to deal with major injury before. Returning to competition, they won junior gold medals at the 2018 Golden Spin of Zagreb in December and at the Toruń Cup in early January. At the 2019 U.S. Championships, they outscored Avonley Nguyen / Vadym Kolesnik by 1.48 points to become national junior champions. The Greens concluded the season at the 2019 World Junior Championships. In the rhythm dance, Caroline stumbled during the tango pattern dance segment, leading to an eighth-place finish. They improved in the free dance, moving up to seventh place. Following the end of the competitive season, Gordon decided to retire from competitive ice dance in order to focus on academics, while Caroline opted to continue skating. On June 20, it was announced that she teamed up with Michael Parsons, the 2016 World Junior champion.
2019–20 season: Debut of Green/Parsons
Moving to the senior level, Green/Parsons placed fifth at Lake Placid Ice Dance International and the 2019 CS Lombardia Trophy. Making their senior Grand Prix debut as a team, they placed seventh at 2019 Skate America. Green remarked that the transition to the senior level had "definitely been mainly adapting to longer programs and more demanding elements. I think that it is a challenge that I am ready for." Competing the following week at the 2019 Skate Canada International, Green/Parsons again placed seventh. They won their first international medal, a bronze, at the 2019 CS Warsaw Cup behind Lauriault/Le Gac of France and Russia's Konkina/Drozd. Competing at their first U.S. Championships, Green/Parsons placed fifth in the rhythm dance. They were fifth in the free dance as well, despite a fall. Parsons said afterward that they were "still a very young team, but it's coming along faster than I ever expected. I couldn't be more proud, I am very happy."
