He was re-elected as leader of the Oslo Conservative Party in 2014 and 2016 before stepping down in 2018, when he was succeeded by Heidi Nordby Lunde.

[3] Ahead of the election in 2013 Astrup was nominated as the second candidate for Oslo, behind the Minister of Defence, Ine Eriksen Søreide.

Following the Liberal Party's entrance into the Solberg cabinet, Astrup was appointed minister of international development, the first person to hold the post in six years.

[6] In his capacity as minister, Astrup was appointed by United Nations Secretary General António Guterres in 2018 to the High-level Panel on Digital Cooperation, co-chaired by Melinda Gates and Jack Ma.

[7] After the Christian Democratic Party entered government on 22 January 2019, Astrup was appointed minister of digitalisation, the first of its kind.

In the final vote, he lost to Carsten Staur, who won the support of 16 members in the ballot compared to Astrup's 13.