Crozier was educated at the Glasgow School of Art (1949-53). On graduating he spent time in Paris and Dublin before settling in London, where he quickly gained great notoriety for his work. A year after his first show with John Wright and William Irvine at the Parton Gallery, Soho, in 1957, Crozier found a studio out in the village of Pebmarsh, North Essex, inspiring his paintings of dark dramatic landscapes, and was invited to show at first the Drian Gallery, shortly followed by Arthur Tooth & Sons with whom he had his first solo show in 1960. In 1963 he spent a pivotal year in southern Spain with the Irish poet Anthony Cronin and the following year the Arts Council included his paintings in the exhibition Six Young Painters with David Hockney and Bridget Riley among others. Crozier taught at the Bath Academy of Art, the Central School of Art and Design, the Studio School in New York and finally at Winchester School of Art. In 1973 he became an Irish citizen, having been born to Irish parents, and lived between homes in West Cork and Hampshire. In 1991 the Crawford Art Gallery, Cork and the Royal Hibernian Academy, of which he was an honorary member, curated a retrospective of his work. Crozier was awarded the Premio Lissone in Milan and the Oireachtas Gold medal for Painting in Dublin in 1994. A major retrospective was held at the Irish Museum of Modern Art, Dublin from October 2017 – April 2018.