He was elected the leader of the Bærum Conservatives on 29 November 2021, defeating the incumbent Siw Wikan with 91 votes.

[2] Following Jan Tore Sanner's announcement that he would step down as deputy leader, Asheim was among the favourites to succeed him, alongside Nikolai Astrup and Ine Marie Eriksen Søreide.

After Nikolai Astrup was appointed to the government on 17 January 2018, Asheim succeeded him as the chair of the Standing Committee on Finance and Economic Affairs.

[8] Following the Solberg cabinet's defeat in the 2021 election, Asheim became the Conservative Party's spokesperson for labour and social policy; and Second Deputy Parliamentary Leader.

[10] Asheim served as acting Minister of Education and Research in Solberg's Cabinet from September to November 2017, during Torbjørn Røe Isaksen parental leave.

[13] In March 2021, Asheim proposed an amendment to the University and College Act in the wake of several reports of unfair treatment of students from staff members.

The professor was eventually fired at the end of the month (March 2021), and Asheim praised the university for taking swift action.