Dan Aran grew up in Jerusalem and got his first drum kit at eleven. A year later he enrolled at the Rubin Academy of Music high school, and by the time he graduated at seventeen he was already working the Israeli scene, playing in bassist Avishai Cohen's trio, in guitarist Amos Hoffman's group, with Omer Avital, and in the bands of the American saxophonist Arnie Lawrence, who had moved to Jerusalem in 1997 and opened his own club there. Lawrence stayed a reference point: Aran later recorded one of his tunes and describes him as a former teacher.

Aran moved to the United States in 2001 and enrolled at the New School in New York, graduating in 2004 with a BFA in performance. He fell in with the Smalls circuit in the West Village, the room that had become a second home for the Israeli musicians arriving in New York through those years. His first documented appearance in the club's archive is with the Nick Hempton Quartet on November 21, 2007, and the Hempton bands account for the largest single block of his club work over the next two decades. In June 2007 he made his first record for the club's label, playing drums on and co-producing pianist Harry Whitaker's trio date Thoughts (Past and Present) (Smalls Records SRCD-0026), cut in a single session on June 18 with Omer Avital on bass.

His own debut followed two years later. Breathing came out on Smalls Records (SRCD-0045) in September 2009, and it is not a conventional band record: rather than one working group, Aran assembled a twelve-piece pool and recombined it track by track, so that no two pieces have quite the same instrumentation. Trumpeter Avishai Cohen, saxophonist Eli Degibri and trombonist Jonathan Voltzok carry the horn writing, pianist Art Hirahara anchors nine of the ten tracks, and single appearances by flutist Itai Kriss, trumpeter Ben Holmes, accordionist and pianist Uri Sharlin and bassoonist Gili Sharett give individual tracks their own colour. Four of the ten pieces are Aran originals. The rest run from Ornette Coleman's "The Blessing" and Cole Porter's "I Concentrate on You" to Arnie Lawrence's "I'm So Blue" and a setting of the Yemenite-Israeli composer Aharon Amram's "Gul Lihibib." Reviewers picked up on the restraint: All About Jazz called it "disarmingly pretty, pure in melodic focus," and Pamela Espeland, writing in September 2009, described a leader who "seldom asserts himself" on his own record.

The decade that followed was mostly sideman work, and much of it landed on two labels. For Posi-Tone he played Art Hirahara's trio date Noble Path (recorded January 27, 2010) and two Nick Hempton albums, The Business (recorded October 9, 2010, with Yotam Silberstein on guitar) and Odd Man Out (recorded October 23, 2012). Outside jazz he turned up on Natalie Merchant's double album of poetry settings Leave Your Sleep (Nonesuch, 2010), and he has worked with Stacey Kent, Madeleine Peyroux, Kevin Mahogany, Peter Bernstein, Joe Magnarelli and Wayne Tucker, as well as playing 1920s repertoire with the Michael Arenella Dreamland Orchestra. In 2017 he was one third of Trio Stonk with Hempton and bassist George DeLancey, whose Live at Smalls was issued in the SmallsLIVE catalogue (SL0053).

Since 2017 his steadiest band has been flutist Itai Kriss's TELAVANA, a Latin and Middle Eastern group he has recorded four albums with: Telavana (Avenue K Records, 2018, cut January 31, 2017), Supermoon (2021, recorded February 1 and 2, 2020, with Shai Maestro guesting on keyboards), and the two halves of All Aboard (Volume 1, June 2024; Volume 2, January 2025), both drawn from the same January 2023 sessions and both featuring Amos Hoffman on oud and guitar. That vocabulary fed directly into his second album as a leader. New York Family appeared on December 3, 2018 on his own imprint, The Whistling Puffer Fish, with Kriss on flute, Adam Birnbaum on piano, Luke Sellick on bass, Zafer Tawil on oud, Marcos Lopez on percussion and Jainardo Batista on vocals. DownBeat called it a fascinating record and "a unique blend of jazz, Latin rhythms and Middle Eastern melodies." Aran has continued to lead his own trios, quartets, quintets and sextets at Smalls and Mezzrow, with dated appearances in the club's archive running through May 17, 2026.

Aran is an accompanist's drummer first, and both his leader records are built that way: he programmes the music, picks the personnel and then mostly stays inside the ensemble rather than in front of it. Audiophile Audition placed his playing "in the Bill Stewart tradition of more is more, coloring the canvas with a lot of detail," which is audible in the way he keeps a 7/8 Yemenite figure or a bolero clave moving under a soloist without flattening it into a groove. The range is unusual even by New York standards. He plays straight-ahead alto-saxophone-and-rhythm-section bebop with Nick Hempton, Latin and Middle Eastern repertoire with TELAVANA, and 1920s hot dance music with the Michael Arenella Dreamland Orchestra, and he treats those as one job rather than three. His formative teachers were Israeli-scene figures rather than American ones: Arnie Lawrence above all, whose tune closes the swinging half of Breathing.