Born in England about 1890, Greensmith arrived in Canada in 1912 and settled in Regina, where she began to work in the provincial Treasury Department. In the 1920s she was working in the Attorney General's Department and studying law. She finished her legal studies at the University of Saskatchewan in 1925, and was admitted to the bar that year. In the meantime she had begun to handle administration of soldiers' estates, doing so until the early 1930s (and again after World War II). By the early 1930s she was a provincial Law Officer, remaining so until her death. In 1948 she was appointed a King's Counsel. Involved in the Civil Service Association, especially in its sports programs, Greensmith was an active member of the Regina Civil Service Tennis Club and of the Wascana Winter club. She was also concerned about women's rights and women's place in the community, and often spoke to women's organizations in the province. She died in Regina on May 20, 1951.