She was born in Oslo as a daughter of politician Omar Gjesteby and Ingrid Elisabeth Thoresen.
She had become involved in the Workers' Youth League in her teens, chaired the secondary school branch from 1964 and was a secretary from 1966.
On 4 February 1981 she was promoted to Minister of Trade and Shipping in the so-called "female government" of Gro Harlem Brundtland.
When the second cabinet Brundtland assumed office in May 1986, Gjesteby was State Secretary in the Ministry of Foreign Affairs.
She was a board member of Oslo arbeidersamfunn (1973–1975, 1983–1984), Horten Verft (1974–1983, 1974–1983), Elcon Leasing (1978–1979), Statens driftssentral for administrative databehandling (1978–1979), Oslo Lysverker (1988–1990), Norsk Hydro (1990) SAS Norway (1997–2001), Mint of Norway (2001-2003), HAV Eiendom (2003–present), Statskonsult (2003–present), Norwegian Academy of Music, Veidekke (2004–present), White Buses Foundation (2007–present).
She was the deputy chair of the Guarantee Institute for Export Credits (1993–1995), and chaired the board of directors of the Cancer Registry of Norway (1988–1990), Kommunenes filmsentral (1994–1995), Asplan Viak (1997-2006), Kings Bay (2000-2002), Bjørnøen (2000-2002),[1] and the National Institute for Consumer Research.