Varda was born in Larnaca in 1916.[1] She attended the Pancypriot Commercial High School in Larnaca, where she was a member of the school hockey team, completing her secondary education in 1933.[1]
After leaving school she began working as a secretary in the law firm of Miltiadis Oikonomakis. While working at the firm, she met Miltiadis Varda who worked at the business next door; the two married in 1944.[1] Oikonomakis was childless and encouraged Constantia to study law. After enrolling at the Middle Temple law school in London, she completed a LL.B course by correspondence, graduating in 1957,[1] becoming the second female lawyer in Cyprus.[1] During the second half of the 1950s she was a member of EOKA, a Greek Cypriot guerilla organisation.[2] She defended several EOKA fighters in court.[1]
In the 1960 parliamentary elections Varda was a Progressive Party of Working People (AKEL) candidate for the Greek Communal Chamber in Nicosia, and was the only woman elected to the Chamber.[3][4][2] The Chamber effectively ceased functioning in 1963,[3] and was abolished in 1965.
In 1985 she became president of the Larnaca Bar Association, a position she held until her death in 1993.[1]