One of two children of engineer Ron Driver and his wife Beryl Thyer, Tess Driver began her education at Rose Park Primary School, but ran away from there at the age of about seven. She then went to Linden Park Primary School and, later, Unley High. She went to the University of Adelaide where she graduated with a Bachelor of Arts in English Literature and Asian History. She has since gained a Diploma of Teaching (University of SA), a Tourism Certificate (SA College of TAFE) and a Masters degree in Creative Writing (University of Adelaide, 1998).

At the age of 20 Driver was involved in a motorcycle accident, which destroyed a potential singing career. In 1961, she married Murray Young. She taught in the South Australian Education Department from 1961-5 and the London Inner Education Authority 1966-7. In 1968 she moved to the USA where she created and taught courses in communication and social competence at the Cathy Lord Career and Fashion School in Rhode Island 1968-70 and ran courses in creative drama for African-American and Mexican children in Texas 1971-2.

Back in Australia, Driver ran courses in communication skills and creative drama at the YMCA in Melbourne, then taught again in the SA Education Department before going to Manila, in the Philippines, in 1977. She spent three years in the Education Research Dept in SA 1978-80, then spent time in Bangkok, where she taught puppetry and creative drama while studying the Thai language and Thai life and culture.

Since then she has lived in South Australia, although she travels to Indonesia and America frequently. She has worked as a research analyst for Murray F. Young and Associates (1981-4), served as Executive Officer of the Tourism Industry Council of SA (1984-6) and taught creative writing for the University of the Third Age (1990-1995). She was editor of the Australian Federation of University Women publications, SA Inc during this time and established the Henley Scribblers as an independent, registered group of writers, co-ordinating the group for six years and editing four community writing anthologies. She is on the editorial committee of Graduate Women, the AFUW quarterly publication. She edited the literary publication ARCA in 1960-1 and was editor of student publications (newsletters and handbook) 1960-1 at Wattle Park Teachers' College.

Driver found the manuscript of a novel, Jenifer, written by Jeanne Forster Young (qv), in an old trunk in a shed, and with the help of the Women's Suffrage Centenary committee she had it published for the Centenary of SA Women's Suffrage in 1994.

In 2001, Driver's poetry was used in the libretto of the opera My Love My Life performed as part of the Adelaide Festival.