Arthur Rosser was born on 16 April 1864 in Oystermouth, Glamorgan, Wales, the son of John Rosser, a builder, and his wife, Jane Shepherd. He was brought to New Zealand with his family at the age of eight and spent the rest of his childhood in the Auckland suburb of Newton, where he attended Newton East School and the Newton Academy. On leaving school Rosser entered the building trade. He was working as a carpenter when he married Sarah Louisa Craig at Auckland on 30 November 1886. The couple then lived in Sydney until 1891.
If carpentry was the young Arthur Rosser's occupation, his vocation was labour politics. In 1895 he was elected president of the Auckland Liberal–Labour organisation and in 1896 and 1899 he stood unsuccessfully for Parliament. Defeated in the polls, Rosser also found himself without a job when conservative building contractors blacklisted him. With a growing family to feed, he took up a new career as a union organiser, becoming in the process Auckland's first professional union secretary. In 1899 he organised the flour millers and two years later he followed up this initial success by establishing a cabmen's union. Within 12 years he was involved in the formation of nine unions and was the secretary of no less than 12. In 1913 he was involved with the formation of the short-lived New Zealand Police Association.
Rosser owed much of his success to the arbitration system established by the Liberal government in 1894. Unions needed the services of professional secretaries who had expertise in the seemingly arcane ways of the Court of Arbitration. In this role Arthur Rosser came into his own, and experienced some success in winning wage increases for his craft unions.
With his livelihood dependent on its continued operation, Rosser was a staunch supporter of arbitration. Ironically some of the first blows against the system were delivered by one of his own unions, the Auckland Electric Tramways Union, which struck in defiance of the Industrial Conciliation and Arbitration Act in 1906 and 1908. As the mood within the Auckland labour movement turned against arbitration and towards collective bargaining, Rosser the moderate found himself swimming against a rising tide of militancy. In 1910 he lost control of the Auckland Trades and Labour Council, an organisation he had dominated for a decade. His place as president was taken by the radical socialist Michael Joseph Savage.
As a union secretary Rosser had continued to participate in labour politics. After 1900 he took a major part in establishing in Auckland the Political Labour League of New Zealand (later the Independent Political Labour League), the first New Zealand Labour Party and the United Labour Party of New Zealand. He also continued to seek elected office. In 1908 he was the IPLL candidate for Auckland Central and he stood for the Auckland City Council in 1901, 1903, 1907 and 1913. Only in 1901 was he successful.
Rosser was representative of the moderate wing of the labour movement. Like other moderates he was committed to improving rather than replacing capitalism. He stressed the need for welfare and higher wages rather than socialism. Testimony to Rosser's commitment to the established system was his appointment as a justice of the peace in 1905. He stood in direct contrast to militant 'Red Fed' (Federation of Labour) unionists such as Savage, who supported industrial unionism, collective bargaining and strikes and regarded politics merely as the means to achieving socialism; one militant referred to him as 'Eight pound a week Rosser'. While they mostly favoured the continued sale of alcohol, Rosser was a confirmed 'wowser'.
After the defeat of the Red Feds in the general strike of 1913, Rosser resumed his position as a central figure in the life of Auckland labour. He was secretary of the Auckland tramway union for almost 30 years (1918 to 1947), and in 1927, 1931 and 1933 he stood as a New Zealand Labour Party candidate for the city council, winning election on the third attempt. He was also the author of a weekly 'Trade and labour notes' column in the Auckland Star, writing under the pseudonym 'Industrial Tramp'.
By the end of the 1930s, however, Rosser's star was on the wane. In 1938, standing as an independent, he lost his seat on the council. A year later, because he had stood against Labour municipal candidates, he was expelled from a Labour Party which had come to be dominated by many of his old militant foes – including Savage, now prime minister. In the last 15 years of his life Rosser found himself an outcast from the movement he had helped to build. He died at Auckland on 15 February 1954, survived by three daughters. Two other children had predeceased him, and Sarah Rosser had died in 1937.