Doron Tirosh started on classical piano at six and let it go, then picked up drums at fourteen and did not let that go. His first teacher was Gal Sivan; two years later he moved to the drummer Shai Zelman specifically to work on jazz. The decisive room was the music track at Alon High School for the Arts, where the pianist Amit Golan taught him and then hired him. Tirosh has said that joining the school's jazz department is when he started practising in earnest and decided he wanted to do nothing but play music for a living, and playing in Golan's trio while still a schoolboy is what put him inside the Israeli jazz scene rather than beside it. At eighteen he made his first professional recording, a disc called Sababa underwritten by the Jerusalem Municipality as a culture-promotion project, with two players who would later turn up in the New York Latin and jazz circuit, the flutist Itai Kriss and the pianist Jack Glottman. At twenty he went back to fundamentals with Alon Bor, a percussionist in the Israel Philharmonic Orchestra, drilling snare technique and reading.

The band that carried him out of the country came together in Jerusalem. Tirosh was playing in the representative jazz quartet of the academy there, and a trio split off from it made up of Alon High School graduates and named for its guitarist: the Yotam Silberstein Trio. It worked steadily across Israel and in Europe, including the Red Sea Jazz Festival and the Cinematheque Festival, and in July 2003 it recorded The Arrival for the Barcelona label Fresh Sound New Talent, released the following year as FSNT 185. The personnel is a snapshot of a Tel Aviv generation about to scatter: Silberstein on guitar, Gilad Abro on bass, Asaf Yuria, then eighteen, on tenor saxophone, and Tirosh on drums for all nine tracks. He is also the composer of one of them, the fourth, "I Hate U Blues," which is the earliest piece of his writing anyone can point to on record.

His first New York period followed. He completed three semesters at City College of New York and, more consequentially, spent a year and a half as the house drummer for the jam sessions at Fat Cat, playing there every week. That is where his address book got made: the pianists Sacha Perry and Ray Gallon, the bassist Ari Roland, the saxophonist Chris Byars, the trumpeters Mike Mullins and Don Hahn. He studied privately and steadily in the city with two drummers from opposite ends of the tradition, Charli Persip and Joe Strasser, and took the drum chair in Sheila Jordan's weekly singers' workshop ensemble. In November 2004 he played a Yitzhak Rabin memorial concert with the visiting trombonist Slide Hampton.

Then he went home for several years, and the Israeli record that documents it is Amit Golan's own. Golan, who had founded the Center for Jazz Studies at the Israel Conservatory of Music in Tel Aviv and had not written music in about two decades, finally cut I Decided! over three days in the Conservatory hall, July 19, 20 and 21, 2007, with the New York trumpeter Joe Magnarelli flown in and a band of his own students and young colleagues: Yuria on tenor, Eden Bareket on baritone, Abro on bass, and Tirosh sharing the drum chair with Yonatan Rosen. In the same years Tirosh taught at the Matan music camps and the Ramat HaSharon Conservatory before joining the Israel Conservatory faculty himself, giving private drum lessons and running jazz ensembles, and he played in the bassist Emil Ram's quartet. He also went back to school on the other side of the music, spending four years at the Tel Aviv academy studying classical composition: piano, counterpoint, harmony, reading and transposing, ear training, and writing for classical performers.

He returned to New York in the middle of the following decade, and Discogs dates his current residence there from 2015. In August 2016 the writer Michael Steinman heard him for the first time in a trio with the guitarist Felix Lemerle and the bassist Murray Wall at a restaurant on Bleecker Street, and has written about him repeatedly since. The steadiest of his New York partnerships is with the pianist Michael Kanan, whose trio he has held down at Mezzrow with Aidan O'Donnell in November 2018 and with Pat O'Leary in April 2023. Around that spine sit the kinds of jobs a mainstream drummer in the city actually does: the saxophonist Neil Saidi's New York Sessions for Gut String Records in February 2017, a Lester Young tribute with Kanan, Murray Wall and the tenor player Larry McKenna at the University of Scranton on September 1, 2018, an hour-long recital at City College with Jon De Lucia, Ray Gallon and Gary Wang that November, and a chamber-sized band at the Bushwick club Ornithology in April 2023 with the singer Gabrielle Stravelli, Lemerle, Kanan, Pat O'Leary on cello and Dan Weisselberg on bass.

His one record as a leader came out of that circle and was made quickly. Simply Because It's Winter was recorded by Neal Miner on March 4, 2018 at the Drawing Room in Brooklyn and issued that May on Miner's label, Gut String Records, as GSR 032, billed to Tirosh with Miner on bass and Kanan on piano. It runs six tracks and twenty-six minutes, half of it Tirosh originals: the title tune, "Why Would You Treat Me That Way?" and "For W.B." The cover photograph, by Yoav Trifman, is of Tirosh laughing at the kit, and Felix Lemerle designed the sleeve. Two years later he was back in Tel Aviv for another Gut String date, the saxophonist Ofer Shapira's Lockdown, cut at SnR Studios on August 3 and 4, 2020, in the middle of the pandemic year, with Ofer Landsberg on guitar and Ram Erez on bass.

Tirosh is a melodic drummer in a specific and slightly old-fashioned sense: he tunes and varies the sounds of the kit as if the drums were carrying the tune alongside everyone else, and he plays quietly enough that the pitch of a cymbal or a rim registers as information rather than punctuation. Michael Steinman, who has followed him since 2016, places him in the line of Baby Dodds, Zutty Singleton and Sid Catlett and credits him with a light touch, meant sonically and temperamentally, and with a melodic lyricism equal to that of Kanan and Miner. Tirosh's own account of the job is unglamorous and consistent with what the records sound like: he wants the other musicians to feel good, and he treats steady time and a shared groove as the point rather than the floor. Two things underneath that are worth naming. One is the lineage he studied in, Charli Persip and Joe Strasser as teachers and the Fat Cat and Smalls bebop circle of Ari Roland, Chris Byars and Sacha Perry as his first New York employers, a strain of straight-ahead playing that never went modal and never apologised for it. The other is the four years of classical composition at the Tel Aviv academy, which shows up less in his drumming than in the three tunes on his own record, all of them melody-first and none of them a drummer's vehicle.