Sunna has extensive experience in a variety of legal areas and has worked in that field since 2012, including contract law, real estate, local government, administrative law, tort law, and more. She has extensive experience in litigation and handling cases in court, as well as in dealing with public offices and institutions.

Sunna started her own business, Áss Law Firm, in 2017, which merged with Lögmannstofa Norðurlands in January 2019. Sunna was admitted to the district court in 2014.