Aarum was educated at Agder Musikkonservatorium, the Sibelius Academy in Helsinki, Musikhøgskolan in Gothenburg before he headed for Oslo in 1998. His jazz talent impressed the Oslo jazz community, and he was a popular collaborator within several bands, while he continued studying at Norges Musikkhøgskole and graduated with the thesis “Social differences in the Norwegian jazz sector”.
He led his own Anders Aarum Trio to the debut album «Lucky strike» (2000) accompanied by Mats Eilertsen (bass) and Torstein Ellingsen (drums). In 2002 he received the No-Fear award from Oslo Jazzradio, and followed up with the album «Absence in mind» (2004), where Ellingsen was replaced by Thomas Strønen. The third album of the Trio, «First communion» (2006), included Ole Morten Vågan (bass) and Andreas Bye (drums).
On “Shakin’ Our Souls”, released on Ozella Music (DE) in 2018, he invited the brothers Magne and Ivar Thormodsæter on bass and drums.
In 2023, Aarum released his fifth album, «Oslo Puzzle», recorded with his fellow jam session hosts from the legendary jazz club Herr Nilsen; Jens Fossum on bass and Hermund Nygård on drums.
Aarum has collaborated with Hilde Louise Asbjørnsen since 2004 and has acted as producer, co-composer and pianist on 10 of her albums. In 2023, they released the duo album “Movies & Storie Like This”, with their own compositions.
Been regular pianist/keyboardist in the bands Element, Jazzmob, Nymark Collective, Funky Butt, Mini Macro Ensemble, The Sinatra Songbook, Sigurd Køhn Quartett, Knut Riisnæs Quartett.

Aarum has worked as producer, pianist, composer and/or arranger on more than 100 recordings, among others with Randi Tytingvåg, Gisle Johansen, Julie Dahle Aagård, Heidi Gjermundsen Broch, Christina Bjordal, Majken Christiansen, Nora Brockstedt, Guro Von Germeten, Sigurd Køhn and Ola Kvernberg.

He is 3 times nominated to the Norwegian Grammies with Fossum/Aarum Quartet “FAQ” in 2007, Sigurd Køhn “This Place» in 2005 and with Julie Dahle Aagård “Stompin’ Feet” in 2009.

Currently he performs with his own trio, in addition to Oslo Jazz Ensemble, Paris-Oslo/Petter Wettre, Espen Rud, Tiril Heide-Steen, Hildegunn Riise and Hilde Louise Asbjørnsen, to mention some.

Through the years, Aarum has collaborated with a broad range of fabulous performers, including Sonny Simmons, Leroy Jones, Bertine Zetlitz, Peter Asplund, Nora Noor, Amund Maarud, Vidar Busk, Nora Brockstedt, Ola Kvernberg, Beady Belle, Herb Geller, Jesper Thilo, Roscoe Mitchell, Kevin Dean, Silje Nergaard, Torun Eriksen, KORK, Kaba Orchestra, Ensemble Denada, Klovner i Kamp, Marie Bergman, Tricia Bouttè, Arne Domnerus, Christel Alsos, John Engels, Louis Stewart and Bob Kindered.