Billing was born and grew up in Blackpool in the north-west of England to Emily Clare and George Billing, who went on to become a respected surgeon in Manchester.[1] Clara Billing studied at the Manchester School of Art before undertaking further studies in London at the Royal College of Art and then in Paris.[1] She began to produce medallions, portrait heads and genre figures and groups working in a variety of materials including cement and concrete, as well as painting portraits, landscapes and still-life compositions.[1][2] Between 1913 and 1957, Billing wa a regular exhibitor at the Royal Academy in London and, in the 1920s and 1930s, showed a total of eighteen works with the Society of Women Artists.[1][2] In 1925 she was elected an associate member of that Society in 1925.[1] She also participated in exhibitions organised by the Women's International Art Club, the Royal Institute of Oil Painters and the International Society of Sculptors, Painters and Gravers.[1][3] Billing was a member of the Artists' Suffrage League and produced posters and cards in support of the campaign for women's voting rights.[4]
After living in London for many years in 1925 Billing moved to Blewbury near Didcot and in 1929 married the sculptor Sydney Langford Jones.[1] Her sister, May Billing, (1883–1939), was also an artist active in the Society of Women Artists.[1]