She served as representative of UN Women in Afghanistan from 2012 to 2014 and later in Turkey as designated Regional Director for Europe and Central Asia.

Sólrún started her political career in the Women's List (Samtök um kvennalista), a party she had co-founded in 1982 and later represented in Reykjavík's City Council from 1982 to 1988.

In 2004 Sólrún took a brief leave from politics and instead attended the European Institute, London School of Economics (LSE) as a visiting scholar.

On 19 July 2017, Sólrún began her mandate as the Director of OSCE Office for Democratic Institutions and Human Rights, where she succeeded Michael Georg Link.

[6] In August 2022, Guterres appointed Sólrún to the United Nations fact-finding mission, led by Carlos Alberto dos Santos Cruz, regarding the Olenivka prison massacre in Ukraine.