On 14 November 1865 in Dublin, Murray was consecrated first Bishop of Maitland, (when his cousin Matthew Quinn was also consecrated Bishop of Bathhurst) by Cardinal Cullen. In October 1866 he landed in New South Wales. After taking possession of the see, the ecclesiastical and educational development of the diocese under his auspices were enormous.[2] He introduced the Dominican nuns to Australia in 1867; and the Brigidines in 1883. Murray visited Europe in 1871; and on a second trip in 1881 secured for his diocese a community of Redemptorist missionaries.
Murray's health began to worsen by the mid-1890s and in 1897 he chose Patrick Vincent Dwyer, his protégé, as coadjutor bishop.[1] He celebrated his golden jubilee as a priest in 1902.