After working the years 1926 to 1929 as a junior solicitor, he started his own law firm together with Richard August Riekeles in 1930.
[1] During the Winter War, which lasted from 1939 to 1940, Palmstrøm was a volunteer on the Finnish side, fighting against the Soviet Union.
He returned to Norway to find his country invaded by Germany on 9 April 1940, and Palmstrøm took part in the subsequent fighting.
He was also present at the Nuremberg Trials of 1945 and 1946, and wrote the Report on Germany's Crimes against Norway together with Rolf Normann Torgersen.
[1] He was also one of four Norwegian members of the United Nations War Crimes Commission, together with Jacob Aars Rynning, Erik Colban and Terje Wold.