Arent was born in Görlitz, Prussia, on 19 July 1898. Self-taught, after various apprentice positions he obtained his first theater job in Berlin in 1923 and became a stage designer. He joined the SS in 1931 and the Nazi Party in 1932. The same year, he was one of the founders of the "Bund nationalsozialistischer Bühnen- und Filmkünstler" ("Union of national-socialist stage and movie artists"), which was renamed "Kameradschaft deutscher Künstler" ("fellowship of German artists") after Hitler's rise to power in 1933.
Arent was appointed "Reichsbühnenbildner" ("Reich stage designer") in 1936 and "Reichsbeauftragter für die Mode" ("Reich agent for fashion") in 1939. He designed the diplomatic uniform of the Nazi diplomatic service. In 1944, he was given the rank of SS-Oberführer.
He is listed under 'Kunstlerische Mitarbeiter' in the 1938-39 catalog issued by Porzellan-Manufaktur Allach, Munich.