Fjeldsted finished her stúdentspróf in 1966, qualified in medicine at the University of Iceland in 1973 and finished specific training in family medicine in London in 1979 and has been a practicing family doctor in Iceland since then. She married Valgarður Egilsson, also a doctor, in 1967. They have had four children, three of whom are alive, and 6 grandchildren. Fjeldsted's mother is Icelandic classical composer Jórunn Viðar and her father was merchant Lárus Fjeldsted.
Politics
Fjeldsted was a member of Reykjavík city council for the Independence Party from 1982 to 1994, and of the city executive council 1986–1994. She was a member of parliament 1999-2003[1] for Reykjavík constituency, and deputy member 1995–1999 and 2003–2007.
Fjeldsted was Chairman of the Icelandic College of Family Physicians 1995–1999, Member of Board of the Icelandic Medical Association 1997–1999, Head of the Icelandic delegation to CPME since 2000, elected CPME Vice President for 2006–2007 and 2008–2009 and elected treasurer 2010–2012.
