Cobb's career has lasted for over forty years which mostly consists of guest appearances on television shows. Her first credited role was in an episode of Star Trek entitled "By Any Other Name", which was first broadcast on February 23, 1968. She was the only female Redshirt to be killed in the original series. She played the matriarch of the Pembroke family on the first season of the television sitcom Charles in Charge, and appeared on the short-lived television series The D.A..
Her film career has included roles in The Second Coming of Suzanne (1974), Just You and Me, Kid (1979), The Runnin' Kind (1989), Lisa (1990), Defending Your Life (1991) and Dr. Jekyll and Ms. Hyde (1995). She also appeared in the TV movie versions of Salem's Lot (1979) and Brave New World (1980). As a stage Actress, she won the L.A. Drama Critics Award for her role in a stage production of Arthur Miller's play After the Fall.
She has been married four times. Her fourth husband was the actor James Cromwell whom she married on May 29, 1986; the marriage ended in a divorce in 2005.
