At Indiana University, since 2015 Meyer has taught sports law and public policy, consults on matters impacting student-athletes, and lectures on Title IX, amateurism, and other ethical issues in sports. Meyer advocates the power of sport to bring about social change. Her focus is on achieving gender equality, diversity, inclusion, safety, and integrity in sports through education, activism, and litigation.

Meyer began her legal career as an attorney in the Bureau of Competition, Federal Trade Commission, in Washington, D.C. She moved to private practice in 1981 and joined Simpson Thacher & Bartlett in New York City. Meyer established Simpson Thacher's Los Angeles office in 1995 and returned to the New York office in the fall of 1998. At Simpson Thacher, Meyer has represented clients on antitrust and sports issues throughout the U.S. including briefing in the U.S. Supreme Court. Currently she focuses on pro bono clients with matters involving gender, sports and education. She is most actively engaged in Title IX litigation on behalf of high school girls.

Meyer is active on a variety of non-profit boards seeking gender equity and fairness in sports, including the National Women's Law Center and the Women's Sports Foundation. Meyer is a member of the Sports Lawyers Association and numerous antitrust and sports committees at the city, state, and federal levels. She also serves on sports advocacy committees for several non-profit organizations. She has been named multiple times a New York Super Lawyer in the categories of Antitrust and Top Women Lawyers and received the Distinguished Alumni Award from O'Neill in 2014.