Clara May Parker, teacher and author, the daughter of John Lewis and Sarah Elizabeth (Wilson) Parker, was born in Aubrey, Texas, in 1879. She received her elementary and secondary schooling in Denton County and then attended North Texas State Normal College in Denton, from which she received a teacher's certificate in 1902. She began her teaching career at high schools in Graham and Wichita Falls. In 1913 she joined the faculty of North Texas. She held leadership positions in several local women's groups, including the Woman's Shakespeare Club and the Young Women's Christian Association. Until 1919 she taught English and Latin at the Denton college, where she was also dean of women. Throughout her career Parker used summers and occasional leaves of absence to pursue studies at the University of Texas, the University of Chicago, the University of California, and Columbia University. She subsequently received three degrees from the University of Texas: a bachelor's in 1913, a master's in 1920, and a doctorate in 1930. Soon after receiving her master's degree she published an article on modern poetry in the Texas Review.
Clara Parker became one of the earliest women to serve on the faculty of the School of Education at the University of Texas in Austin when she was hired in 1919 as an adjunct professor in the Department of the Art of Teaching. By the time of her retirement in 1946 she had been promoted to full professor (1935) and made a member of the graduate faculty (1943). She specialized in directing practice teachers of English and Latin and served in 1945 as acting chairman of her department (by then known as Curriculum and Instruction). She also had distinguished herself as a leader in a variety of teacher's groups, especially those for women. She was instrumental in founding the Faculty Women's Club and also helped organize and served as first president of the Austin branch of the American Association of University Women. Her other professional activities included memberships in the Texas State Teachers Association, the Modern Language Association, the American Association of University Professors, Phi Beta Kappa, and Pi Lambda Theta.
Parker was invited in 1929 to become a founding member of Delta Kappa Gamma, a new professional society for women teachers; she postponed membership until her doctoral work was completed but later served four years as president of the Austin chapter and provided services as songwriter, poet, and editor for the group nationally. In 1949 she wrote a brief biography of the founder of Delta Kappa Gamma, Annie Webb Blanton. The work was a pioneering effort to record Blanton's contributions as an educator. Also through Delta Kappa Gamma, Parker assisted in compiling Pioneer Women Teachers of Texas (1952). After retiring, she pursued her hobbies of folk dancing and antique collecting. She was a lifelong Baptist. She died in Austin on December 15, 1958. Her fiancé had been killed in the Spanish-American War, and Clara Parker was never married; she was survived by two nephews and one niece. Her funeral was held in Austin; she was buried in Pilot Point, Denton County.