Eve Muirhead (Stirling, SCO) finished 6-7 in the 0 team LGT World Women's Curling Championship qualifying round, held April 30 - May 9, 2021 in , . In their opening game, Muirhead defeated Tabitha Peterson (Chaska, USA) 10-6, then won 10-5 against Sayaka Yoshimura (Sapporo, JPN) and 7-6 against Daniela Jentsch (Fuessen, GER). Muirhead went on to lose 7-6 against Yu Han (Beijing, CHN). Muirhead lost 8-4 to EunJung Kim (Gangneung, KOR). Muirhead lost 7-4 to Anna Hasselborg (Sundbyberg, SWE) where Muirhead responded with a 9-6 win over Stefania Constantini (Trentino, ITA). Muirhead won 6-5 against Anna Kubeskova (Prague, CZE). Muirhead went on to lose 6-5 against Kerri Einarson (Gimli, CAN). Muirhead lost 10-6 to Silvana Tirinzoni (Aarau, SUI) where Muirhead responded with a 8-5 win over Marie Turmann (Tallinn, EST). Muirhead went on to lose 9-8 against Alina Kovaleva (St. Petersburg, RCF). Muirhead lost 9-5 to Madeleine Dupont (Hvidovre, DEN) in their final qualifying round match.
 
Muirhead ranks 130th overall on the Year-to-Date rankings with 0.000 points earned so far this season.