Glenn began learning to skate in 2004. She won a bronze medal at the 2013 Junior Grand Prix event in the Czech Republic and became a national junior champion at the 2014 U.S. Championships. Ranked fifth in the short program and eighth in the free skate, she finished seventh at the 2014 World Junior Championships in Sofia, Bulgaria. She trained in McKinney, Texas and at Stonebriar Ice in Frisco, Texas until the rink closed in 2014. In May 2014, U.S. Figure Skating named Glenn as the recipient of the 2014 Athlete Alumni Ambassador overall award. In August, she won bronze at the 2014 JGP in France. She finished sixth at her second JGP assignment, in Estonia, and 13th on the senior level at the 2015 U.S. Championships. Glenn began the 2015–2016 season training in McKinney, Texas under Ann Brumbaugh and Ben Shroats. After placing fifth at the 2015 JGP in Latvia and sixth on the senior level at the 2015 Skate Canada Autumn Classic in mid-October, she decided to take a break to "reevaluate". She resumed training in February 2016 after joining Peter Cain and Darlene Cain in Euless, Texas. Glenn placed fifth at the 2016 CS Nebelhorn Trophy, fourth at the 2016 CS Golden Spin of Zagreb, and eighth at the 2017 U.S. Championships. She was selected to compete at the 2017 World Junior Championships but withdrew in early March. Glenn finished eighth at the 2017 CS Lombardia Trophy. She was invited to compete at her first Grand Prix event, the 2017 Cup of China, after the withdrawal of Gracie Gold. She placed tenth in China, and finished the season with a second consecutive eighth-place at the 2018 U.S. Championships. Glenn was sixth at the 2018 CS Lombardia Trophy, and seventh at the 2019 U.S. Championships. Competing on the Challenger series again at the start of the 2019–2020 season, Glenn won the bronze medal at the 2019 CS U.S. Classic. This was her first senior international medal. Assigned to two Grand Prix events, she placed seventh at the 2019 Skate America and sixth at the 2019 Cup of China. She was fourth in the short program at the 2020 U.S. Championships with a clean skate and, remarking on her then-recent coming out, said it "has brought a weight off my shoulders. It was very scary, and not having to pretend I’m someone I’m not anymore. She dropped to fifth place after the free skate, and said further mental preparation was needed. Glenn finished ninth at the 2020 Four Continents Championships, her first senior ISU championship assignment.
