Before entering politics, Cournoyea was an announcer and station manager for CBC North in Inuvik, and a land claims worker for the Inuit Tapirisat of Canada, now Inuit Tapiriit Kanatami.

Cournoyea served as premier until 1995, and subsequently chose not to stand for reelection to the Legislative Assembly.

In 2008, she was made an Officer of the Order of Canada[2] as well as inducted into the Aboriginal Business Hall of Fame.

The Truth and Reconciliation Commission's report described how she was sheltered by Aboriginal families along her route when she ran away from an Anglican hostel in the Northwest Territories after a confrontation with a teacher.

[4] In 2023, Canada Post announced that Cournoyea will be one of three people, alongside George Manuel and Thelma Chalifoux, honoured as Indigenous pioneers on new postage stamps.