Inga assumed the office of Minister of Education and Children on 11 January 2026. She served as Minister of Social Affairs and Housing from 21 December 2024 to 11 January 2026.

She has been a Member of Parliament for the Reykjavík South Constituency since 2017 (People’s Party).

Inga founded the People’s Party in 2016 and has been its chair since its establishment. She has served on the Consultative Committee on Fishing Fees since 2018; the Industrial Affairs Committee 2017–2018 and 2022–; the Budget Committee 2018–2021; the Procedural Committee 2019–2021; the Preparatory Committee for the Review of Election Credentials 2021; and the Election Credentials Committee 2021.

Member of the Icelandic Delegation to the West Nordic Council 2017–2020, and the Icelandic Delegation to the Nordic Council 2020–2021.