Ziv Taubenfeld was born in 1986 in Karmiel, in the Galilee, and came to music through his primary school orchestra, where he started on the clarinet at eleven. After primary school he took classical lessons with Ilya Schwartz at the Karmiel conservatory, and it was there, following what he calls an attraction to low sounds, that he added the bass clarinet as a second instrument. It became his main one and has stayed that way; he has never built a career on the higher horn.

The turn from classical training toward improvisation came through the Israeli saxophonist Albert Beger. Taubenfeld's own account is that meeting Beger opened a road, and the road led out of Israel: Beger's introduction took him to the Netherlands, where he read for a bachelor's degree in the jazz programme at the Prins Claus Conservatorium in Groningen and studied bass clarinet with the American reed player Michael Moore, who had been resident in Amsterdam since the early 1980s. Moore has since become a fixture in Taubenfeld's own bands rather than a former teacher, playing on every Full Sun record.

He had already formed the group that would carry him for a decade. Bones, a trio with two other musicians from Karmiel, the bassist Shay Hazan and the drummer Nir Sabag, was assembled at home and recorded its first album in Amsterdam in May 2015, at the studio of the guitarist Niels Brouwer. Leo Records issued it as Bones in February 2016. Everything the trio played was Taubenfeld's writing, and the format, bass clarinet over double bass and drums with no chordal instrument and no second horn, put his tone at the centre of every piece. In September 2016 the Bimhuis in Amsterdam gave him a Carte Blanche, an evening to programme as he liked, and he used it for Bones and for a second, unrecorded band of Dutch improvisers called Plots. The invitation that followed took Bones to the North Sea Jazz Festival in July 2017.

Two more Bones albums came out of that period. Haberdashery, recorded live at the Bimhuis on October 1, 2016 and released by Leo in September 2017, has eight of his compositions arranged by the trio. Reptiles, cut at Splendor in Amsterdam on November 14, 2017 and pressed by the Lithuanian label NoBusiness Records as 300 LPs in October 2019, splits its seven tracks between written material and three unaccompanied bass clarinet pieces. John Sharpe, reviewing it for All About Jazz, described the record as skeletal but attractive.

Alongside the trio, Taubenfeld became a working member of the Amsterdam improvised music scene and its satellites. He joined Kuhn Fu, the guitarist Christian Achim Kühn's jazz and rock band, formed in Groningen in 2012, and has played bass clarinet on every one of its records from Live At Atelier Il Sole In Cantina (2014) to Katastrofik Kink Machine (2024), including the Saalfelden double album and the EP Tantalos, whose title piece was nominated for the German Jazz Prize in 2023. He works in the guitarist Henk Zwerver's groups Zwerv and Zyft, in the nine-piece Owlman, and in the Xavier Pamplona Septet, whose 2019 record sets repertoire by Guus Janssen, Tristan Honsinger and Fred Katz next to a horn improvisation credited to Taubenfeld, Moore, Alistair Payne and Giuseppe Doronzo.

His own large ensemble arrived in 2019. Full Sun, a flexible group rather than a fixed band, debuted at the Bimhuis on January 9, 2019 under the concert title "Ziv Taubenfeld's Spider Jungle," with Moore, the trombonist Joost Buis, the Portuguese trumpeter Luís Vicente, the Argentine pianist Nicolas Chientaroli, Hazan on double bass and Onno Govaert on drums. The Polish label Multikulti Project released the tape as Ziv Taubenfeld's Full Sun in October 2020. A second album, Out Of The Beast Came Honey, taped at Splendor on October 10, 2020 with Omer Govreen replacing Hazan, came out on the Portuguese label Clean Feed in June 2022. Both are entirely his compositions, and several of the pieces are dedications: "Tchicai" for John Tchicai, "MoonDoctor" for Jemeel Moondoc, "Blues For Sunny" for Sunny Murray. The group has also played as an octet with the Senegalese griot Dudù Kouate, and has performed a live soundtrack to Fritz Lang's silent film Der müde Tod.

In July 2023 he returned to Tel Aviv to record with Beger for the first time on album, eighteen years after Beger's own first meeting with the American drummer Hamid Drake. The quartet of Beger on tenor saxophone, Taubenfeld on bass clarinet, Hazan on guimbri and double bass and Drake on drums taped two sessions, one at the Tel Aviv club Levontin 7 on July 10 and one at Kitcha Studios on July 8. NoBusiness released the four pieces as Cosmic Waves, with liner notes and a poem by Taubenfeld. The label and Beger date it May 27, 2024; Discogs gives June 6, 2024.

He has since left the Netherlands for Portugal, a move already visible in his Lisbon recording connections: the Creative Sources catalogue, Ernesto Rodrigues's octet and Variable Geometry Orchestra, and a trio with the cellist Helena Espvall and the drummer João Sousa that recorded at Namouche Studio in Lisbon on March 4, 2024 and released You, Full Of Sources And Night on NoBusiness in November 2025. Two months earlier he had started his own label, Full Sun Records, whose first release is the septet album Nomads, recorded at the Bimhuis and issued in September 2025 as a hundred hand-assembled CDs. Its liner note, signed in Lisbon in July 2025, names Duke Ellington, Sun Ra and Misha Mengelberg as the masters whose paths the group is walking.

Taubenfeld plays the bass clarinet against its recent history. Writing in the Free Jazz Collective, Vid Jeraj described his approach on Out Of The Beast Came Honey as showing anti-Dolphean intentions: he mostly declines the overtones and altissimo leaps that Eric Dolphy made the instrument's signature, working instead with multiphonics in the middle register and a raw, unpolished tone that Martin Schray singled out as the thing that stands out in the ensembles he plays in. Mark Corroto, reviewing the Lisbon trio for All About Jazz, still reached for the same comparison from the other side, hearing in the record a glimpse of the paths Dolphy might have gone on to explore. The four musicians he names as his influences are Don Cherry, Bill Dixon, Jimmy Lyons and Sunny Murray, which is a first-generation free jazz list rather than a bass clarinet one, and it shows: his interest is in group sound, not in the instrument as a display case. As a composer he writes short, clear frames and lets the players stretch them, a habit Eyal Hareuveni characterised as compositions containing hints of chamber music, haunted atmospheres and contemplative moods, and Jeraj heard as rooted in Third Stream writing with a cinematic edge. The dedications running through his catalogue point the same way, to Tchicai, Moondoc, Murray, Lyons, Sonny Simmons and Mal Waldron, and the Nomads liner note adds Ellington, Sun Ra and Mengelberg alongside the polyphonic singing of the Central African forest peoples as the material the septet was working from.