Kempson is a writer, director, and performer. Her plays have been presented in the United States, Germany, and Norway. As a performer, Kempson has toured internationally with Nature Theater of Oklahoma, New York City Players, and Elevator Repair Service. She is a MacDowell Colony Fellow, a member of New Dramatists, a USA Artists Rockefeller Fellow, an Artist-in-Residence at the Abrons Arts Center, a 2014 nominee for the Doris Duke Impact Award, the Laurents Hatcher Award and the Herb Alpert Award, and a New York Theatre Workshop Usual Suspect. In 2015, Kempson launched the 7 Daughters of Eve Thtr. & Perf. Co. at the Martin E. Segal Center at the City University of New York. She has taught at Sarah Lawrence College, Brooklyn College, and the New School.