In the Summer of 1949 Crozier enrolled at Glasgow School of Art where he studied Painting and Drawing under Mary and William Armour, and David Donaldson. At the School of Art Crozier became enthralled by existentialism in the writings of Jean-Paul Sartre and the surrealist poets, notably Paul Eluard.  In Glasgow he discovered the works of Edvard Munch in the 1952 touring exhibition of paintings to Kelvingrove from Oslo. This enthusiasm was not shared by his tutors. Donaldson declared ‘Munch? I prefer mince’ but Crozier had already left behind the conservative ethos of Glasgow School of Art. In 1950 he had met ‘the Roberts’, Colquhoun and MacBryde, and his first public exhibition at the Carnegie Library in Ayr showed the influence of Picasso refracted through the paintings of the two older Scottish artists.

On graduating in 1953, Crozier left for London, though he continued to return to Glasgow. An enthusiastic follower of the avant-garde productions at the Citizens Theatre, he was friends with the artists Pierre Lavalle, Louis Mazzaroli and Donal Bain, In Edinburgh he sought out  the poets Hugh Macdiarmid, W.S.Graham and Sydney Goodsir Smith.

In the 1950s Crozier was part of the artistic and literary society of Soho where he mixed with artists such as Francis Bacon, Colquhoun and Macbryde and Gerald Wilde. Equally important were his friendships with the writers George Barker, Elizabeth Smart, Paul Potts and the Irish poets, Patrick Kavanagh and Anthony Cronin. 

A lifelong pacifist, Crozier spent 1954-56 in Dublin to avoid conscription, There he made a threadbare living as a scene painter at the Gaiety and Olympia theatres while continuing to develop his art. Dublin also deepened his friendships with the poets, Kavanagh and Cronin, John Montague and Derek Mahon. 

On his return to London, he began to exhibit at the Artists’ International Association, the Institute of Contemporary Arts and, from 1958, at the Drian Galleries, a centre for European abstract art in London. He began to establish his reputation for a form of abstracted landscape. In these brooding images, inspired by rural Essex and the drab gardens of suburban London, Crozier discovered he could use landscape less for its topographical interest than as a means to convey intense human emotion and experience. His were landscapes forged by an existentialist world view and the nuclear threat of that time, but also by his interest in the abstract painting of Soulages and Hartung in Paris, and the American abstract expressionists on view in London in the 1950s. He was also close to those English artists among his contemporaries who were developing the language of abstraction, notably Gillian Ayres, Terry Frost and Roger Hilton.

Crozier had combined painting with art school teaching since the late 1950s, first at Bath Academy of Art, (with Howard Hodgkin, Henry Munday and Terry Frost), then  from 1965 at the Central School of Art and Design (with William Turnbull and Cecil Collins), at the Studio School in New York and, significantly, at Winchester School of Art where he was Head of the Fine Art department. There he led a distinctive centre for painting based on the European tradition and set up pioneering agreements with art departments in Spain, France and Ireland that would ultimately become formalised as the first ERASMUS programmes in Fine Art. 

In the late 1960s, Crozier turned his attention again to creating an image of man in the 20th Century. He wrote "I would like an art which is as a razor slash" and he made a remarkable series of skeletal paintings, influenced by his visits to the sites of Auschwitz, Belsen and Ravensbrück concentration camps. These paintings, which the artist considered to be among his most important works, were also a response to ‘the Troubles’, the civil war then being played out in Northern Ireland. Crozier became an Irish citizen in 1973.

Writing on Crozier's use of skeletal figures, Philip Vann has commented; for Crozier, ‘The skeleton is still very much a sentient human being: vulnerable, dignified, alone and abandoned in a landscape of astonishing beauty.' This series of visceral skeletal images can now be seen to anticipate the 'New Expressionist' German painters of the 1980s, and in 1975 Crozier was grouped alongside Francis Bacon in the important exhibition, Body and Soul at the Walker Art Gallery, Liverpool.

Soon afterwards, in 1988, Crozier accepted a contract with the Scottish Gallery, with whom he had several solo exhibitions in London and Edinburgh, one of which, entitled ‘The End of the Modern World’, responded directly to the eponymous poem by Anthony Cronin, whom the artist had lodged with during his formative experiences in Alhaurin el Grande 20 years before.  In 1990, he returned with Cronin to the Spanish village to film Radio Telefis Eirean’s documentary entitled ‘The Truth about a Painter’. 

Throughout the 1980s and 1990s Crozier’s landscapes are inspired by what he described as his "almost visionary' experience of the places that meant most to him, depicting West Cork and southern England in radiant colour. Crozier set out to create images in which, as he said, landscape is 'the vehicle through which I can express intangible things, things which have no narrative. Loss, memory - all can be done through the language of landscape." From the mid-1990s, landscape forms became more abstracted and monumental and he began to use still life to explore new relationships between the natural forms in the composition.