Heiða Árnadóttir has focused her career on the performance of modern music, folk, jazz, experimental works, and lied music. Heiða completed her Master's degree in classical singing at the Royal Conservatory in The Hague. In addition to numerous concerts in Iceland, where she has premiered various compositions with Ensemble Adapter and Caput, Heiða has also performed in the Netherlands, Belgium, France, India, Sweden, and Denmark.

Her performances include appearances at Nordic Music Days, Iceland Airwaves, Skálholt Summer Festival, Siglufjörður Folk Festival, Reykjavík Jazz Festival, and various international festivals such as WOMEX in Copenhagen. 

Heiða was nominated for the Icelandic Music Awards in the category of "Classical Singer of the Year" in both 2020 and 2022. In 2024, she received "Singer of the Year" at Gríman, the Iceland Performing Arts Awards for her performance in the opera/poetic tale "MÖRSUGUR."

Heiða has composed songs and lyrics and is the vocalist for the band Mógil, which has released four CDs. From 2020 to 2023, Heiða served as the artist-in-residence for the modern music festival "Dark Music Days". 

Additionally, Heiða released a CD and vinyl titled "Tunglið og ég," featuring the music of French composer Michel Legrand, with lyrics in Icelandic, accompanied by pianist Gunnar Gunnarsson.