Dame Dehra was first elected as a Member of Parliament (MP) for Londonderry, as Dehra Chichester (as she was known prior to her second marriage in 1928), in the 1921 Northern Ireland general election. She stood down at the 1929 election just before her second marriage but was elected unopposed as Dehra Parker in the 15 March 1933 by-election for the South Londonderry constituency following the death of her son-in-law James Lenox-Conyngham Chichester-Clark, and served until her resignation on 15 June 1960. Her grandson, James Chichester-Clark, was elected unopposed at the subsequent by-election. He later served as the fifth Prime Minister of Northern Ireland from 1969 to 1971.