Alexander William Jessep was educated at Sale Grammar School, Marshall College Aberdeen Scotland, and the University of Melbourne (first year). From 1915-1920 he joined the 53rd Battery as a gunner and went overseas with the 5th Division, where he saw active service. He was discharged from Caulfield Hospital on 3 January 1920, with the rank of Lieutenant. After the war he was able to resume his studies, and in 1922 completed his Bachelor of Science, University of Melbourne, and Master of Agricultural Science and Diploma of Education, University of Melbourne (1924).

Jessup aquired first placement on November 1926 as a Science Master at Burnley Horticultural College (Burnley School of Horticulture and Primary Agriculture) where he became Principal. He was also a part-time lecturer at the University of Melbourne and Director of the School of Agriculture. From 27 October 1941-27 March 1957 Jessup was the Director of the Royal Botanic Gardens, Melbourne and Government Botanist

Trips and Conferences
1950 Royal Horticultural Society Camellia and Magnolia conference and first heard about the Yunnan reticulates from Professor Yu;
International Botanic Conference, Sweden;
1954 Visited Japan to sudy methods of propagating.
Jessup travelled extensively. In northern Italy, he advised local nurserymen on propogation by cuttings instead of the of slow method of layering. He was the first to import the species 'Camellia Grantamiana' and introduced the first batch of Yunnan reticulates into Australia.
1972 International Camellia Conference Italy and England.

Awards:
1967 E.G. Waterhouse Gold Medal from the Royal Horticultural Society for outstanding service to horticulture, and the society honoured him by making him an Honorary Fellow, a Patron and President Emeritus;
John Pascoe Fawkner Medal for Horticulture;
Waterhouse Medal/T.A. Stewart Memorial Award (by the Rose Socities of Australia/New Zealand) for outstanding service in the interest of roses - highest local award for a rosarian
Farrer Medal for wheat;
1972 Merrillees Gold Medal.

Memberships:
Jessup was a Member of several societies, including:-
1952-1962 Founding Member and First President of the Australia Research Camellia Society, and then Registrar of New Camellia Cultivars;
1924 President of the Rose Society of Victoria (which became the Natural Rose Society of Victoria) for four terms;
Royal Horticultural Society of Victoria Fellow and scientific advisor.

Publications:
For years Jessup supplied the camellia notes for the Garden Lover, a Victorian publication;
Cultivation of Herbs, Plant Hybridization, Camellia Cultivation in Australia, Editor Rose Annual for nineteen years.