Ösp grew up in a valley in North of Iceland with her musical family. Together they would play folk and traditional music and perform professionally together across the country.
In 2010, along with her brother and close friends, they took to the stage as a band called Brother Grass. The folk/americana/bluegrass group released two albums together and gained a loyal following and their song "Draugaboli" was premiered on BBC Radio3.
After studying classical singing and jazz singing, Ösp moved to the city of London in the autumn of 2011 to study further in music and to pursue a solo career. Inspired by the vocals of Ella Fitzgerald, the stories of Joni Mitchell and by her own nordic folk roots, she began to write her own songs which have been described as etherial nordic folk. Her debut album, Tales from a poplar tree was released on March 22nd 2017 and was nominated as the Folk album of the year at the Icelandic Music Awards.
In 2015 Ösp and her long time friends and collaborators Anil Sebastian and Cherif Hashizume (Cherif also co produced Ösp's solo album) formed the band Hrím. The band had its Iceland Airwaves debut in 2019 performing three sold out shows and are now working on their first album.
In the spring of 2020 Ösp and brother Örn ELdjárn formed the band Blood Harmony. To perfect the “Blood Harmony”, which happens when close family members sing together, Örn and Ösp are joined by their younger sister, Björk Eldjárn. The project officially started in the early spring of 2020 when, due to covid19, the trio had all moved back to Svarfaðardalur valley in North Iceland, where they are from. They transformed the basement at their parent’s farm into a recording studio and started recording songs they had written a while ago but for some reason not found the right platform for, until now. So far they have released three singles, Summer Leaves, Wicked Heart and Draumsnillingar (dream masters) and are currently working on a LP album.