She was born in Petropavlovsk, Akmolinsk Oblast, Russian Empire. After musical studies in Omsk in 1927–1931, she transferred to the Leningrad Conservatory, where she studied with Mikhail Youdin. She later continued studies at the Moscow Conservatory with Vissarion Shebalin. After her graduation in 1938, she continued post-graduate studies. These were interrupted in 1941, then resumed in 1944. During her period away from studies, she worked as a staff composer for the Ashgabat Philharmonic Orchestra in the Turkmen SSR.
After the end of the Great Patriotic War, Auster went to the Estonian SSR to study the local folk music. In 1948, Auster was appointed music director of the Estonian SSR Television and Radio Committee. Despite her position, she faced criticism for formalism by Soviet authorities. Nevertheless, she continued to serve in her position until 1984. She was also on the board of the Union of Composers of the Estonian SSR.
Aside from her four ballets, Auster also composed orchestral works, music for the stage, chamber music, and songs, as well as an opera. Conductors who have championed her work include Neeme Järvi, Eri Klas, Roman Matsov, Rostislav Merkulov, Kirill Raudsepp, Alexander Ryabov.