Arthur E. Shipley studied zoology at Christ's College, Cambridge, where he was awarded the degree Bachelor of Arts (BA) in 1884 with first class honours in the natural science tripos. Subsequently he received the degree Master of Arts (MA). He stayed on in the college as a demonstrator in comparative anatomy, became a lecturer on the morphology of invertebrates in 1894, and a reader in zoology from 1908 to 1920. He was elected a Fellow of the Royal Society of London in 1904 and was also a Fellow of the Zoological Society of London and the Linnean Society.
Shipley published extensively on zoological topics. Following an important memoir on worms in the Quarterly Journal of Microscopical Science in 1890 he began his studies of parasitic worms. Eventually he published nearly 50 papers on this subject and established a reputation as a competent researcher. He was joint editor of the journal Parasitology (1908-1914) and with S.F. Harmer edited the Cambridge Natural History (10 vols, 1895-1909), of which he wrote several sections. His books included Zoology of the invertebrata; a textbook (1893), Zoology, an elementary textbook (1901, with E.W. McBride) and a number of more popular works such as Pearls and parasites (1908), The minor horrors of war (1915), Life, a book for elementary students (1923) and Creation by evolution (1928).
Shipley became a member of the British Association for the Advancement of Science in 1887 and served on its council from 1904. The next year he came to South Africa to attend the joint meeting of the association with its South African counterpart, as joint vice-president of Section D (Zoology). On 14 August 1905 he was one of the speakers at a ceremony to award certificates to part-time students at the South African College, Cape Town. During the next few weeks he gave an evening lecture in Pretoria on fly-borne diseases, malaria, sleeping sickness, etc. His contribution to the joint meeting consisted of a demonstration of Ankylostoma (Hookworm) preparations, based on his studies of parasitic worms.
Shipley travelled much, including several visits to the United States. On one of these visits Princeton University conferred an honorary Doctor of Science (DSc) degree on him in 1906. During later years he was active in the administration of the University of Cambridge, serving, among others, as vice-chancellor from 1917 to 1919. He did much public work as a member of various committees and commissions, and was awarded the Knight Grand Cross of the Order of the British Empire (GBE) in 1920.