Geeson's first major film appearances were in To Sir, with Love (1967) alongside Sidney Poitier and pop singer Lulu and in Berserk! (also 1967) co-starring Joan Crawford. She followed these films with the comedy Here We Go Round the Mulberry Bush (1968). Geeson became well known as a result of a regular role on the BBC early-evening soap opera The Newcomers. She also had a major role in the mid-70s costume drama Poldark as Caroline Penvenen (later Caroline Enys).
Geeson's other films include Prudence and the Pill (1968), Three Into Two Won't Go (1969), 10 Rillington Place (1970), Doomwatch (1972), Brannigan (1975), starring John Wayne, with whom she enjoyed working), and The Eagle Has Landed (1976). In the TV series Danger UXB (1979), she played the female lead, Susan Mount, opposite Anthony Andrews. She also had the lead role of Fulvia in the science fiction series Star Maidens (1976).
In the 1970s, Geeson lived with set designer Sean Kenny until his death in 1973. Geeson was married to actor Kristoffer Tabori from 1985 until their divorce in 1989. In a 2015 interview, Geeson stated that she had resided in Los Angeles, California, for the past 30 years.
In addition to her film and television work during this time, Geeson also performed in theatrical productions for the Royal Shakespeare Company as Lavinia in Titus Andronicus and as Viven 532 in Section Nine (both 1973). She also had roles in stage productions of Next Time I'll Sing to You (1980) and The Real Thing (1985), both in London, before making her Off-Broadway debut in The Common Pursuit in 1987.
In the 1980s, Geeson appeared in several stage productions, including two for the Royal Shakespeare Company, as well as an Off-Broadway production of The Common Pursuit (1986). After relocating to the United States, she returned to television, playing the recurring character of Maggie Conway on the American series Mad About You from 1992 until 1999, as well as a recurring role on Gilmore Girls in 2002. In 2012 and 2016, she appeared in Rob Zombie's The Lords of Salem and 31, respectively.
In 1984, Geeson relocated from London to Los Angeles, California, where she began appearing in American television, including a role as a series regular on the sitcom Mad About You, playing the hostile neighbour, Maggie Conway, from 1992 to 1999. She also played the role of Sandrine in the Star Trek: Voyager episodes "The Cloud" and "Twisted".
