Hope was elected a Fellow of the Royal Society of Edinburgh in 1788 and served as its vice president from 1822 to 1833.
In 1791 following the death of his uncle, Alexander Stevenson, Hope succeeded him in his uncle's role as Professor of Medicine at Glasgow University.
In 1795 Hope was selected by Joseph Black as his assistant (1795–1799) and eventual successor to the professorship of medicine and chemistry (1799–1843) at the University of Edinburgh. Hope’s goal was to more fully combine the practice of medicine with his chemical instruction.
In 1796 Hope was elected a member of the Harveian Society of Edinburgh and served as President in 1800 and 1816. 
In 1800 Hope won the annual Edinburgh Arrow archery competition.
In 1804 he became a member of the Highland Society.
In 1805 he was elected a member of the Aesculapian Club.
In May 1810 he was elected a Fellow of the Royal Society of London.
From 1815 to 1819 he served as President of the Royal College of Physicians of Edinburgh.
Between 1824–40 Hope worked with scientists based in Poissy, France. With the town's major, Jean-François Senincourt, he tried to establish a university in the town. Within a few years their aims began to be realised as medical students crowded his lectures.
In 1828 he gave £800 to found a chemistry prize at the University of Edinburgh.
In the 1830s he is listed as living at 31 Moray Place, a large townhouse in the Moray Estate on the western edge of Edinburgh's New Town.
In 1843 he resigned the professorship. He died at his home, 31 Moray Place in Edinburgh's West End in 1844.
He is buried in Greyfriars Kirkyard in central Edinburgh. The grave lies against the western wall of the original churchyard, towards the north-west corner.