Rapp eventually became the Supreme Commander of the Swedish Armed Forces in 1961, a position he held until 1970, overseeing substantial changes in military organization.

Rapp became a member of the board for the Defence Forces Central Civilian Employee Office (Försvarsväsendets centrala civilanställningsbyrå) on 1 January 1938 and division commander of the F 2 Hägernäs in 1938.

Rapp was a member of the 1942 Reserve Officer Experts (1942 års reservbefälssakkunniga) from June to November 1942 and he became a major in the Swedish Air Force on 1 July 1942 and a lieutenant colonel on 1 April 1944.

Rapp became Vice Chief of the Air Staff on 1 October 1948 and was a member of the Swedish Armed Forces School Study from June 1950 to March 1952.

He became acting head of the Aircraft Department of the Royal Swedish Air Force Materiel Administration on 1 July 1956 and became a member of the board of the National Aeronautical Research Institute in 1957.

[1] During his time on the post, major changes were made to the Swedish defense, including an enhanced coordination between the army, the air force and the navy.