Kristrún was born in Reykjavík, and her parents are Frosti Fífill Jóhannsson, an ethnographer, and Steinunn Guðný H. Jónsdóttir, a doctor.

[1] She has worked as a journalist for the business newspaper Viðskiptablaðið and has been an employee in the analysis department of Arion Bank.

She served until 2021, when she applied to be on the Social Democratic Alliance list in the Reykjavík South constituency.

[3][4] Kristrún led her party into the 2024 snap election, securing 20.8% of the vote and 15 seats in the Althing.

[5] She held coalition negotiations with the Viðreisn and People's Party which began on 4 December and concluded seventeen days later, when she was appointed prime minister along with her cabinet.