Hadar Noiberg was identified as having absolute pitch at six and got her first flute at ten. The training that followed was entirely classical: she played in the Young Philharmonic Orchestra, studied flute at the Tel Aviv academy with Yossi Arnheim, the principal flutist of the Israel Philharmonic Orchestra, and with Prof. Uri Shoham, and took composition with Slava Ganelin, the Lithuanian-born pianist who had co-founded the Ganelin Trio before emigrating to Israel. At 21 she transferred to the City College of New York, where she finished a bachelor's degree in flute and composition and studied composition with David Del Tredici. In 2007 the ASCAP Foundation gave her an award for composition. She has put her New York arrival at age 21 and her time in the city at fifteen years; in a March 2018 interview she said she had lived there for thirteen years, which places the move around 2005. The Jerusalem Post gave her age as 32 in August 2015.

What she did with the classical degree was leave the concert hall. In New York she worked charanga bands, Moroccan Andalusian ensembles and Brazilian choro groups, joining the choro collective Regional de NYC; she has dated her discovery of choro to 2005 and has since played Rio de Janeiro, Sao Paulo, Belo Horizonte and Brasilia, and appeared with the Brazilian guitarist Yamandu Costa's quartet at the Red Sea Jazz Festival in Israel. Her sideman log runs through the same range. She plays flute on the 2011 debut by Yemen Blues, the Yemenite-and-funk band Ravid Kahalani founded with the bassist Omer Avital, where her flute sits in a front line with Itamar Borochov on trumpet, Avi Lebovich on trombone and a cello and viola pair. In the same year she is on the Brooklyn funk band The Pimps of Joytime's Janxta Funk!. Later credits include the drummer Allison Miller's Otis Was A Polar Bear (Royal Potato Family, 2016), the Colombian composer Juan Andres Ospina's Tramontana (2018), Cool Down by Bernard Purdie & Friends (Sugar Road, 2018), where she is billed among the special guests, and the Live At Dizzy's album by the guitarist Romero Lubambo with the Rafael Piccolotto Chamber Orchestra (Sunnyside, 2021), on which she doubles flute and piccolo.

Her own band is a trio with no chord instrument in it: flute, double bass, and drums or percussion. She calls it her harmony-less trio and has been explicit about the argument behind it, that the flute in Western improvised music has usually belonged to doublers or been treated as a secondary voice, while in the Eastern traditions she draws on the ney and the bansuri are central instruments. The first record, Journey Back Home (2010), put Omer Avital on double bass and oud and Ziv Ravitz on drums. By her own account the session was booked as a demo, was only the third time the three had played together after two rehearsals, and most of what was cut that day became the album. From the Ground Up followed on Dot Time Records (DT9041) in 2015, with Haggai Cohen Milo on bass and Allison Miller on drums, Anat Cohen guesting on clarinet and Yotam Silberstein on guitar on three tracks. Reviewing it for Jazz da Gama in May 2016, Raul da Gama called her technique nimble, her tone sweet and her phrasing elegant.

Open Fields, released April 28, 2018 on the Belgian label Jammin'colorS, is the record that carried furthest. It was cut at Studio42 in Brooklyn with Eduardo Belo on double bass and acoustic guitar and Amir Bar-Akiva on drums, engineered and mixed by Alessio Romano and mastered by Alex DeTurk, with the Spanish pianist Chano Dominguez guesting on two of the nine tracks. Kerilie McDowall reviewed it in DownBeat in September 2018, describing an expressive finesse across sharply defined, well-crafted and flowing compositions and singling out the title track's pairing of flute with guitar. The program mixes originals with the Israeli song "Na'ama."

The Dominguez guest spot turned into a working duo. Paramus came out on Sunnyside (SSC 1564) on November 8, 2019, eleven tracks that set her originals against Paco de Lucia's "Cancion de Amor" and the Ladino folk song "Morenika," pulling her Israeli material and his Andalusian flamenco vocabulary into the same room. A second duo record landed the same year: The Hawk, made with the German pianist Olivia Trummer for the Stuttgart label Flavoredtune (FTR361906 on CD in 2019, FTR361306 on vinyl in 2020), eight tracks produced, mixed and mastered by Michael Fetscher, with four Trummer compositions, two by Noiberg, a Shmulik Kraus song and George Harrison's "Here Comes the Sun."

Teaching has since taken up as much of her calendar as touring. She built a method called The Self Sufficient Flutist, aimed at flutists from any genre who were never taught rhythm, harmony or improvisation, and has run it online and in workshops for about five years, using choro as the entry point for classically trained players. In the autumn of 2024 she toured it through the United States, with stops at the Alabama School of Fine Arts on October 10, the Flute Center of Chicago on October 12, the University of Minnesota on October 14 to 16, the University of Michigan on October 21, Seattle and Portland from October 24 to 27, and San Jose on November 1. Her sixth leader or co-leader record, Zero Point, a duo with the pianist Katia Toobool, appeared on August 29, 2025 with nine tracks including "For Turiya," "Firenze" and "Mozart Reimagined." Her own site notes it was submitted for Grammy consideration. She has been listed as an artist of Trevor James flutes and, elsewhere, as a Haynes ambassador clinician.

The defining choice in Noiberg's music is the missing chord instrument, and everything else follows from it: with only bass and drums under her, the flute carries both the melody and the harmonic implication, and she has used electronic effects and sampled loops to widen the instrument's range rather than adding a piano. Her collection of antique wooden flutes and low flutes, alto and bass, feeds directly into that, giving her registers a concert C flute cannot reach. The vocabulary underneath is a genuine mixture and not a garnish: Middle Eastern and North African rhythmic cycles, Brazilian choro phrasing, Cuban charanga, Andalusian flamenco through her work with Chano Dominguez, all sitting inside jazz improvisation and Western harmony. She has named her influences as instrumentalists and singers rather than flutists, citing Dexter Gordon, John Coltrane and Stevie Wonder, and has said that letting jazz mix with other traditions is what keeps the style alive. DownBeat has reviewed her twice, calling Open Fields a captivating, uplifting listen and, in Matthew Kassel's March 2020 notice, describing Paramus as a lovely duo record, delicate and deeply felt. Discogs files her leader catalogue as Jazz.