Priestman was born in Bradford, Yorkshire to a wealthy Quaker family in the textile industry. His father was an enthusiastic art collector and his uncle, the painter Arnold Priestman (1854-1925), gave him lessons in the holidays. On leaving school he began an engineering course at Bradford Technical College but soon abandoned it to study at The Slade School of Fine Art. There he remained for two terms, taught by Alphonse Legros (1837-1911) amongst others before becoming a studio assistant to Sir William Llewellyn (1858-1941), later President of the Royal Academy. 

Priestman began exhibiting and painting professionally in the last decade of the nineteenth century. He had a painting selected for the Royal Academy in 1890 but his work leaned more to the modern and the post-impressionist young turks of the New English Art Club. He showed regularly there and with the International Society and the New Gallery, taking a studio in fashionable but bohemian Chelsea in 1891. During this period he was taken up by two influential art collectors Alexander Young and James Staats Forbes. His ‘English Impressionism’ aligned with continental tastes of the period and he received an Honourable Mention for his exhibit at the Paris Salon in 1900 and the Gold Medal at the Munich International a year later.

In 1914 Priestman purchased ‘Windy Haugh’ at Walberswick, Suffolk, adding a studio where he took in pupils. He remained their almost continuously until 1927, counting Edward Seago amongst his students, a friendship that lasted his lifetime. Throughout his career he seems to have split his time living and working between the North and East Anglia. On the outbreak of war he was based in South Westmorland but later exhibited from addresses in Snape Hall and Woodbridge. He was a familiar figure in his 1908 vintage De Dion Bouton touring East Anglia on his annual painting trips after the War.

Priestman was a well-regarded portrait painter but above all he is remembered as a landscape artist. His views of his native Yorkshire and the towering skies of East Anglia won him many admirers, including Sir Frank Brangwyn who described him as “the finest sky painter of our day.”

Public collections who hold his work include the Yale Center for British Art, the National Museum of Wales, Kirklees Museums and Galleries, Paisley Museum and Art Galleries, Worcester City Art Gallery, the Ferens Gallery, Hull, the Walker Art Gallery, Liverpool, the Royal Academy of Arts, London, Bristol Museum & Art Gallery, Newport Museum and Art Gallery and every civic museum and art gallery in the North of England worth mentioning.

In 1981, thirty years after his death, Bradford and the Ferens Art Gallery in Hull staged a major retrospective of his work.