A minor official's son, he went to Gymnasium and completed his military service as an "Einjährigfreiwilliger" ("one-year volunteer"). Thereafter he served at the front between 1914 and 1918 in the First World War, where he was seriously wounded in 1915. When the war ended, Klausner was made a first lieutenant. Having served in the Volkswehr between 1919 and 1920, he joined the Austrian Federal Army in 1920. In 1922, he joined the Austrian Nazi Party, which he left in 1927, after the ill-fated Beerhall Putsch. In 1930 he was promoted to major – the highest rank that he would reach in the Austrian Army before he had to leave for health reasons in 1933.
In February 1931, he once again joined the NSDAP, which won influence in local council and provincial elections in Carinthia in 1931 and 1932. Klausner was appointed acting Nazi Gauleiter in January 1933 and four months later, in May 1933, he took over as Gauleiter the leadership of the still-outlawed Nazi Party in Carinthia. In the time of the Austrian Ständestaat, Klausner was interned in 1936 for a few months for political reasons, which did not, however, keep him from doing further work for the Nazi movement, nor even from joining the SS, in which he was given the rank of Oberführer.
After Anschluss with Nazi Germany, Klausner was appointed by Arthur Seyß-Inquart on 13 March 1938 to be the Minister for Political Decision Making in the first National Socialist cabinet, and on 22 May of the same year he became Reichskommissar Josef Bürckel's deputy, as well as Austrian interior minister at the same time.
Along with all this, he also held, as of 1 June 1938, the office of Gauleiter of Carinthia. Hubert Klausner died suddenly on 12 February 1939 in his flat in Vienna of a stroke. Adolf Hitler even showed up at Klausner's state funeral in Klagenfurt, and he delivered the commemorative address.