As of 1 April 1933, Klemm became a full professor and head of the Department of Inorganic Chemistry at the Technische Hochschule Danzig. Klemm replaced Hans Joachim von Wartenberg, who had taught at the Technische Hochschule Danzig from 1913 to 1932 and served in several senior positions including head of the Department of Inorganic Chemistry. Von Wartenberg left in August 1932 to become director of the Institute of Inorganic Chemistry at the University of Göttingen.
The Technische Hochschule Danzig was at that time located in the Free City of Danzig (1920-1939). The population of the city was predominantly German and faculty and staff tended to align with National Socialism even before 1933. The attitudes of scientists at the university have been described in terms of "shades of gray".
Klemm had some involvement with the National Socialists but his motives are not known.
Klemm was not a signatory of the Bekenntnis der Professoren an den deutschen Universitäten (1933). 
He did sign the later Aufstellung zu den Unterzeichnern des Appells „An die Gebildeten der Welt“ (11. November 1933), a list of academics who professed support for Adolf Hitler and National Socialism. Klemm became a member of the NSDAP (Nazi Party) in 1938, rather later than contemporaries like Adolf Butenandt.
Following the Invasion of Poland which began 1 September 1939, the Free City of Danzig was annexed by Germany, and anti-Jewish measures escalated.
In a letter to the editorial staff of Chemische Berichte in June 1942 Klemm argued that contributions from chemist Georg-Maria Schwab and other "non-Aryan" authors should not appear in German chemical journals.
Klemm served as head of the Inorganic Chemistry department of the Technische Hochschule Danzig from 1933 to 1945, and was its last vice-rector.  He was responsible for the evacuation of equipment, books, files, and people in 1944–1945, in advance of Soviet troops. Approximately 500 books and pieces of equipment and 300 staff and family members sailed on the ship Deutschland on 27 January 1945 bound for Kiel.
Much of the university including the chemistry building was destroyed in subsequent months.  Following the war Gdańsk became part of Poland. On 24 March 1945, the university was re-established as a Polish institution.