Eick was born in the village of Hem in Norway, in 1979. He is the brother of he brother of the jazz musicians Johannes Eick and Trude Eick. He took up piano at five and switched to trumpet a year later. His father and mother were both musicians and there were instruments all across their family room. Eick attended the Trondheim Music Academy where he studied trumpet and bass. He attended high school at Toneheim Folkehøyskole with music as his central focus of study, and attended later Trondheim Musikkonsevatorium where he majored in jazz studies. He played in many local rock and jazz bands and made several recordings as a sideman.
In 2000 he joined the virtually unclassifiable Jaga Jazzist and played on their album A Livingroom Hush in 2001. He also took on session and live work with several Norwegian artists including Motorpsycho, metal supergroup Arcturus, and The Gathering. In 2004, Eick made his debut with ECM as a session player on guitarist Jacob Young's Evening Falls, and also played on Iro Haarla's Northbound. In 2005, Jaga Jazzist released the acclaimed What We Must. In 2007, Eick did more work for ECM: He played with Young on the guitarist's Sideways and appeared on drummer Manu Katche's star-studded Playground. He also played on Ulver's Shadows of the Sun, and Music for a While's Weill Variations. That year, the International Jazz Festivals Organization presented Eick with the annual International Jazz Talent award.
In 2008 Eick issued The Door, his leader debut for ECM. His sidemen on the date included Stian Carstensen on pedal steel, Jon Balke on piano and electric piano, Auden Erlien on bass and Audun Kleive on drums. The set drew rave reviews on both sides of the Atlantic and sold well in Europe. He toured Europe and returned in 2009 to play on albums by Youn Sun Nah (Voyage) Inger Marie Gundersen (My Heart Would Have a Reason) and Silvertongue (Diamond Sky). He also won the national Statoil Scholarship, the largest arts scholarship in Norway. In 2010, Eick played on Motorpsycho's Heavy Metal Fruit and bluesman Mighty Sam McClain and Mahsa Vahdat's Scent of Reunion: Love Duets Across Civilizations. Jaga Jazzist released their acclaimed One-Armed Bandit that year as well.
In 2011, Eick worked with Haarla again on her universally lauded Vespers with Trygve Seim, Ulf Krokfors, and Jon Christensen. He also released his sophomore ECM date Skala, offering a more contemporary pop-oriented sound in nine original compositions. Uncharacteristically, producer and label boss Manfred Eicher allowed him to co-produce the album. Already prolific, Eick contributed to no less than seven albums in 2012 including Motorpsycho's The Death Defying Unicorn, with Mighty Sam McClain w/ Mahsa Vahdat on A Deeper Tone of Longing: Love Duets Across Civilizations, and Alexander Von Mehren's Aéropop.
The following year Eick played a lengthy headliner's tour of Europe and an abundance of dates as a performing sideman. Still he found time to work in the studio. He and vocalist Elvira Nikolaisen issued the contemporary jazz ballads collection, I Concentrate on You for Grappa. Jaga Jazzist's Live with Britten Sinfonia appeared that year too. In 2014, Eick's recording schedule proved hectic: He performed on no less than seven recordings including albums by Lars Danielson, Tania Saleh, and the Eple Trio. His own Midwest was issued by ECM in 2015, performed by his quintet with pianist Jon Balke, violinist Gjermund Larsen, percussionist Helge Norbakken, and bassist Mats Eilertsen. Critically acclaimed, it made year-end best-of lists across the globe. Eick spent the rest of the year anfd part of 2016 touring Europe. He also managed session work, playing on albums by Beady Belle and Nathan Sykes, among others. While the trumpeter played select dates in 2017, they took a back seat to an intense period of session work as he appeared on no less than eight recordings, including Kari Ikonen's Ikonostasis, Kåre Kolve's live set Interactions at Vossajazz, and Danielson's Libretto 3.
In the spring of 2018, Eick issued his fourth album for ECM. Entitled Ravensburg (after the home village of his grandmother), it was the first of his recordings to find him doing double duty on trumpet and vocals. He was accompanied on eight original compositions by violinist Hakon Aase, pianist Andreas Ulvo, electric bassist Audun Erlien, and drummers/percussionists Thorstein Lofthus and Norbakken. That year he also appeared on Chick Corea and the Trondheim Jazz Orchestra's What Game Shall We Play Today, and Batagraf's Delights of Decay. The following year he wrote "No Storm" for Tora Augestad and played on her album Dialogue.
In September 2021, Eick released When We Leave, his fifth leader outing for ECM. Recorded over two days in November 2020, it featured a septet with violinist Hakon Aase, pianist Andreas Ulvo, Erlien on bass, Lofthus and Norbakken on drums, and Carstensen on pedal steel. ~ Matt Collar, Thom Jurek, Rovi