Upon completing her undergraduate studies, Penrose was offered a post by
Agnes Maitland, the principal of Somerville, designed to keep her at the college as a combined tutor, librarian and secretary, but instead moved to London. She taught for a short time as an extension lecturer in Oxford and London before being appointed as Principal of
Bedford College in 1893. She was given the additional post of Professor of Ancient History in 1894, "without additional stipend". According to
Margaret Tuke's history of the college, "It is a tribute to her character and statesmanship that, in spite of the limited sphere accorded to her by the authorities, she should have accomplished so much in so few years." During Penrose's time as principal, the students' social life developed as their numbers increased, Penrose had also introduced an entrance examination for students seeking to join Somerville in 1908, making it the first women's college to do so. She was responsible for adding additional tutors, including
Helen Darbishire and
Margaret Hayes Robinson to the Somerville staff, and enabled tutors to become part of Somerville's council for the first time in 1921. and a member of the
Royal Commission on the Universities of Oxford and Cambridge in 1919. Penrose became the statutory commissioner for the University of Oxford in 1923. ==Service in World War I and retirement==