After leaving school at 18, Frank Rossiter Crozier worked for an Italian decorator for a short period, embellishing the interiors of churches. He then worked as a bank clerk for eight years and attended life drawing classes in the evening three times a week. He studied under the cartoonist Alek Sass and attended the National Gallery of Victoria School of Art in Melbourne, studying full-time from 1905 to 1907. Crozier received the student prizes for landscape and drawing in 1907.
When the First World War broke out, Crozier enlisted with the Australian Imperial Force (A.I.F.) in March 1915. He arrived in Egypt in May 1915 and at Gallipoli in September 1915, where he served as a stretcher-bearer with the 22nd Battalion.
In November 1915, official war correspondent Charles Bean, called for contributions for The ANZAC Book, a collection of soldiers satirical and sombre accounts of their experiences at Gallipoli. Crozier was working on illustrations for The ANZAC Book during December 1915 when Bean asked him to design the more serious content of the Book.
In March 1916, Crozier arrived in Marseilles, France where he was attached to the 1st ANZAC Corps Topographical Section. Crozier continued as a private in Pozières until October 1917. In France he served under Brigadier-General John Gellibrand who, after realising Crozier s artistic ability, asked him to make sketches of the Battle of Pozières. General Gellibrand had Crozier serve as his runner, partly so he could be exposed to a wide variety of painting subjects.
In October 1917, Crozier was transferred from the 1st ANZAC Corps Topographical Section and was attached for three months to the Australian War Records Section (AWRS) at the AIF Administrative Headquarters in London. Crozier had successfully applied to the AWRS to work as one of ten camouflage artists. He was trained in camouflage work in London with Will Longstaff, J. S. MacDonald and James Scott. In September 1918, he was appointed an Official War Artist with the rank of honorary lieutenant.
Crozier was one of the few artists in the AIF who had experienced heavy fighting, as at Pozières, and also served in the infantry at Gallipoli. The effect this had on Crozier is revealed through his choice of subject matter; he frequently painted the human dimension of warfare.
Following the First World War, Crozier continued to work for the AWRS in London. Crozier returned to Australia in late 1919. His commission as an Official War Artist was terminated in June 1920. He was appointed to the Australian War Memorial in May 1936 in an art advisory role, a post he held for six months. During the Second World War Crozier worked in a munitions factory at Maribyrnong, Victoria.