Tessa Shaw, the daughter of Sierra Leone attorney-general Oliver Shaw, graduated from the Guildhall School of Music and Drama in London, later earning an honours degree in psychology from London University. Pursuing a career in acting, her first credited role for television was her appearance in Doctor Who, after which followed appearances in Doomwatch (created by former Doctor Who production staff members Kit Pedler and Gerry Davis) and Fox, which also featured Eric Mason, Bill Nighy and Patricia Quinn. In 1990, she appeared in a guest role on Press Gang, a program upon which future Doctor Who head writer and executive producer Steven Moffat served as co-creator and sole writer.
Her first son, actor Daniel Fathers, was born in 1966 from her relationship with West End scenic designer George Fathers. A second son, conservationist Jason Fathers, and a daughter, consultant Emma-Louise Fathers (later Cluskey) followed some years afterwards. In 1989, she got married to film producer Richard Winter-Stanbridge.
She currently resides in Los Angeles with her husband.