Gleeson was educated at Glen Innes and Dubbo Primary Schools, Dubbo High School, and Sydney University. She graduated with an Arts (Honours) degree and Diploma of Education. After teaching high school English and History, she travelled overseas, where she taught English and English as a Second Language (ESL) in Italy and London, between 1976 and 1980. During this time she wrote her first children's book Eleanor Elizabeth, which included reflections of Australia and of ideas and feelings from her childhood.
On returning to Australia, she continued to teach ESL as well as consulting in teacher-training for the University of New South Wales from 1981 to 1985. Full-time writing in 1986 and 1987 was possible because of consecutive Fellowships from the Literature Board of the Australia Council, and again in 1991.
Gleeson is actively involved in writers' organisations. She espouses the importance of literary groups because of their positive effect on her own writing. Gleeson writes fiction for older readers, younger readers and picture books as well as articles. Her works are frequently reviewed in newspapers, and periodicals.
In 1997 Gleeson received the Lady Cutler Award for Distinguished Service to Children's Literature. Her writing has been short-listed for, as well as receiving, a variety of awards, reflecting the wide appeal of her literature.