A resident of Charlottetown, Labrador,[4] Dempster has worked as an employment counsellor and as a municipal Councillor in Charlottetown, including serving as the town's deputy mayor.[4] Dempster is a member of NunatuKavut.[5]
After her re-election in the 2015 election, Dempster was named Deputy Speaker of the House of Assembly.[6] She was promoted to Minister of Children, Seniors, and Social Development in a cabinet shuffle on July 31, 2017.[7]
She was re-elected in the 2019 provincial election.
On August 19, 2020, Dempster was appointed Minister Responsible for the Status of Women and Minister of Indigenous Affairs and Reconciliation, Minister of Labrador Affairs, and Deputy Government House Leader in the Furey government.[8][9]
She was re-elected in the 2021 provincial election.[10] On July 19, 2024, she was appointed as Minister of Environment and Climate Change, Minister of Labrador Affairs, Minister Responsible for Labour, Minister Responsible for Workplace NL, and Deputy Government House Leader.[11]