Claire Davison was born in Boulder, Colorado. Davison received her initial ballet training at the Boulder Ballet School on full scholarship. She attended the Boston Ballet School, Pacific Northwest Ballet School, School of American Ballet and San Francisco Ballet School summer programs on scholarship. Davison was awarded third place at the Denver Ballet Guild Young Dancers Competition and was a finalist at the Youth American Grand Prix competition in New York City in 2009. Davison was recognized as an international Young Medalist and performed at the International Ballet Festival of Miami. She joined the Jacqueline Kennedy Onassis School at American Ballet Theatre in 2010 and received the Ron and Toby Altman scholarship at that time.
Davison joined ABT as an apprentice in November 2012 and became a member of the corps de ballet in June 2013.