Alice Eleanor Cossey was born on 8 November 1879 at Drury, Auckland, New Zealand, the eighth of nine children of Solomon Cossey, a shoemaker, and his wife, Martha Bragg Martin. She inherited an interest in industrial affairs from her father, who was an ardent Liberal–Labour supporter. While she was apprenticed to Alf Gifford, a master tailor, and starting out as a tailoress, Cossey lived in Auckland, attending Sarah Heap's physical culture classes in her spare time.
In 1917 Alice Cossey became the secretary of the Auckland Tailoresses' Union (ATU), a position she was to hold for 28 years. She was one of the first professional female unionists in New Zealand in a generation that included Mabel Howard and Jane Runciman. Except for a short time around 1938, she presented all the union's award cases to the Court of Arbitration. She was a grass-roots organiser who worked hard building the weak Auckland union into the strongest: membership rose to over 1,500 by 1922 (although it dropped to a low point of 965 in 1934 during the depression). It was usual for Cossey and her assistant, Ada Anderson, and later Jean Sunder, to go around factories in the lunch hour once a month to collect union dues. Some employers and many workers were disagreeable, and in 1917 Cossey admitted to the president of the New Zealand Federated Clothing Trade Employees' Association, J. T. Paul, that she was 'only green at this game'. However, she quickly improved and became adept at persuading other women's organisations to assist her union. In June 1918, for instance, she got the Auckland Women's International and Political League members to distribute notices of an address by Paul to women and girl whiteworkers (who made underclothing) at their factory gates.
As ATU secretary, Cossey embarked on three major national campaigns on the behalf of working women. She led the protest against the closing, for reasons of economy, of the Department of Labour's women's employment bureaux in 1920. The government was inundated with protests after Cossey wrote to all women's organisations asking them to complain. Cossey was a leading advocate of higher wages for women. In 1922, before the Court of Arbitration in Wellington, she argued against wage cuts for women. She was active in opposing the way in which unemployed women were treated during the depression and in orchestrating the ATU's resolutions and mass meetings against government policy. She was a member of the deputation from the Trades and Labour Councils of New Zealand April 1931 conference that waited on Prime Minister George Forbes. Her role was to represent unemployed women and those on reduced wages. In addition to arguing for sustenance for women – who paid an unemployed tax but received no relief payments as men did – she pointed out that 2,500 women in the clothing industry alone were working a four-day week. She feared that without government intervention doss-houses for women would appear. Limited relief was provided.
Throughout the inter-war period, Cossey used a number of union forums to publicise her causes, from the wrongful dismissal of women to the need for more female factory inspectors. As ATU representative, she joined the unemployment committee, which the Auckland Trades Hall co-ordinated in 1926, and, in 1931, the Auckland Unemployed Women's Emergency Committee, comprising representatives of all women's organisations. However, she became increasingly disillusioned with the emergency committee's ineffectualness and in 1931, together with Miriam Soljak and Alice Basten, resigned in protest. She was one of two women among 30 men who sat on the Auckland Trade Union Secretaries' Association, and was the ATU delegate on the Auckland Trades and Labour Council until the height of the depression, when her union withdrew, probably for financial reasons. The ATU rejoined the clothing federation in 1934, which it had left earlier, possibly as a costs-saving measure.
Under Alice Cossey's leadership the ATU was never involved in a strike. Her moderation was typical of that of other tailoress activists and her support of arbitration put her in conflict with male leaders such as John Roberts. She kept the ATU out of the One Big Union movement, an amalgamation of men and women from all regions, because although women outnumbered men three to one in the tailoring industry, men dominated the combined unions. Thus Cossey ensured her union survived as a women's union. In 1945 she threatened to pull the ATU out of the clothing federation as 'a protest against the attitude of the federation towards the Women's Unions' and a rise in membership fees. She questioned whether the federation was acting legally and was outraged that Roberts said he would 'go on with the amendments whether they are right or wrong'. Nor did his telling Cossey that he would like her job if she thought of leaving endear him to her. Cossey won the battle, although there was a second fight in 1949 when Flo Humphries unsuccessfully took out a legal action against the ATU for alleged 'undemocratic procedures'.
As a consequence of her local and national standing, Cossey was made a justice of the peace in 1931. She deferred her retirement until after the Second World War, during which she was heavily involved in the wartime direction of labour, especially appeals by tailoresses who resented being assigned to other jobs. When she retired in 1945 she left behind a strong union which was the oldest surviving women's union in New Zealand. About 1925 Cossey, who remained single, had returned to the old home where she was born in Creek Street, Drury, to live with her two unmarried sisters, Martha and Georgina. She commuted by public transport into the city for over a decade before buying a car in 1938 and driving daily. In later life she gardened and learnt embroidery. Alice Cossey died aged 90 on 14 March 1970 and was buried in the Drury cemetery.