Greeves was elected to Armagh County Council soon after she returned to Ireland from France. She joined the Ulster Women’s Unionist Association in 1925, taking on multiple roles over the years, including senior vice-president in 1975. She was motivated to get involved in politics “after seeing the conditions in the institution in the city”. One of her first jobs was as secretary of Portadown Infant Welfare, a position she held for over 30 years. Her political work encompassed health, welfare and education. She established an infants' welfare centre, of which she became honorary secretary. She was chair of the Armagh County Welfare Committee from 1947 to 1969. She was also a member of the town planning committee and in 1965 spoke in support of establishing a university in Armagh. In 1963 she was the first woman to be elected chair of the Northern Ireland Association of County and County Borough Welfare Committee, having previously been the vice-chair. In 1972 she was elected to the new Southern Health and Personal Social Services Board. She was also vice-chair of the Armagh County Health Committee. In 1965 Greeves featured on a TV show, ‘Lady in Question’, talking about her “life in the front line of battle.” In 1966 she was reported as speaking out against the docking of horse tails, which had been outlawed in the 1952 Protection of Animals Act, but evidence of the practice had been seen at the annual
Balmoral Show.
Senator Greeves was the first woman to be elected to the Senate of Northern Ireland, as an independent member, on 20 June 1950, serving until 1969. In 1964 she was cited as “the lone figure standing for the rights of women against the 25 male senators”.{{cite news |date=1958-11-21 |work=Belfast News Letter |author=Olive Kay ==Girl Guides==