Fischer was born in 1987 in London, England, but grew up in Amsterdam. Her father was conductor Iván Fischer, and her mother was recorder player Anneke Boeke. Beginning at age 15, Nora sang with the Netherlands' National Youth Choir for seven years. Fischer enrolled at the Amsterdam Conservatory but repeatedly clashed with her teachers and was ejected after a single semester. She switched to the University of Amsterdam, studying philosophy and musicology, but returned to singing and earned a degree at Copenhagen's Complete Vocal Institute in Denmark. Fischer went on for a master's degree at the Royal Conservatoire of The Hague in New Audiences and Innovative Practice. At her debut performance, she cooked food for her audience. She has named avant-garde soprano and Luciano Berio collaborator (and spouse) Cathy Berberian as a major influence.
Fischer made her recording debut in 2016 on the album Iván Fischer: A Composer's Portrait, devoted to her father's music. In 2017 and 2018, she made a 15-city tour under the auspices of the ECHO Rising Stars concerts. Fischer has performed with major ensembles and presenters that are mostly but not exclusively oriented toward contemporary music, including the Los Angeles Philharmonic, the Kronos Quartet, and the Dutch National Opera. She has appeared at such prominent venues as Walt Disney Hall in Los Angeles and the Philharmonie de Paris, and she frequently tours with the Silk Road Ensemble created by cellist Yo-Yo Ma. In 2018, Fischer made her solo recording debut on Deutsche Grammophon with Hush, a collection of Baroque arias on which she was accompanied by electric guitarist Marnix Dorrestein. She moved to Signum Classics in 2019 for The North Wind Was a Woman: Chamber Works by David Bruce and to Nonesuch in 2020 for the album Louis Andriessen: The Only One, featuring a song cycle written for her shortly before Andriessen's death. ~ James Manheim, Rovi