He served at the Organization Department of the Air Staff from 1 June 1935 to 1938 and became a captain in the Swedish Air Force on 30 June 1937. 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. He was acting head of the Organization Department of the Air Staff in 1941 and became head on 1 July 1943. 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.