[3] Arup was also involved in politics, and in 1836 he was elected into the Norwegian Parliament (Stortinget) for Drammen constituency, where he was reelected in 1839, 1842 and 1845.

[4] He was later appointed temporarily councillor of state in interim for the Norwegian government in Sweden in the years 1852–53, 1857 and 1861.

In 1860, Arup crowned Charles XV of Sweden king of Norway at Nidarosdomen in Trondheim.

[2][5] He was a proponent of religious toleration for Protestant dissenters as both a bishop and politician, helping to pass legislation towards this goal in 1845.

[4] He was also in favour of greater liberty from the state for the Norwegian church.