Born Countess Feodora Georgina Maud von Gleichen, she was the eldest daughter of Prince Victor of Hohenlohe-Langenburg (a naval officer and sculptor and half-nephew of Queen Victoria) and his wife, Laura. In 1889, she and her two sisters, Valda and Helena, were bridesmaids to Princess Louise and the Earl of Fife.
Gleichen studied art in her father's studio and later with Alphonse Legros at the Slade School of Art. She completed her studies in Rome in 1891 and regularly exhibited at the Royal Academy from 1892. A bas-relief and hand-mirror in jade and bronze won her a bronze medal at the Exposition Universelle in 1900.
In 1917, Gleichen was granted the rank and style of a daughter of a marquess by Royal Warrant of Precedence following the reforms of the family names of George V. She died, unmarried, in 1922 at her grace and favour apartment in St James's Palace. Shortly before her death, she was awarded the Légion d'honneur and was later posthumously made the first woman member of the Royal British Society of Sculptors.