Austad attended the Jazz program at the Norwegian University of Science and Technology in Trondheim (NTNU), and received a Bachelor's degree in jazz performance. Later he earned a Master's degree in Music teaching at the Bergen University College (Hib). He has been working as a freelance musician since the mid 1990s and has played in different musical settings and with musicians like Kjetil Møster, Thomas T. Dahl, Frode Alnæs, Sigurd Køhn, Elisabeth Lid Trøen, Ole Hamre, Håkon Mjåset Johansen, Frank Jakobsen, Ernst-Wiggo Sandbakk, Magne Thormodsæter, Signe Førre, and Sigvart Dagsland. His main jazz projects are his own Eivind Austad Trio and the jazz quartet Living Space, fronted by the saxophonist Kjetil Møster.