From an early age, like her cousin Estrid Hein, Carstensen took a special interest in the status of women in the community.[1] In 1906, she was a co-founder of Foreningen til Hjælp for enligtstillede (Association for Supporting Single Mothers) but went on to devote most of her time to the Danish Women's Society. In 1907, she replaced Astrid Stampe Feddersen as head of the society's voting rights committee but failed to persuade all the other women's organizations interested in voting rights to join the Women's Society.[2]
From then on, she became a leading member of the organization, serving as vice-president from 1913 to 1918. In addition, from 1908 to 1913, she edited the Society's journal Kvinden & Samfundet, working with Thora Daugaard as editing secretary. Not only did she display fine editing skills, she became an effective contributor to the journal herself.[1][2]
As local branches of the Women's Society were created, Carstensen headed the Copenhagen chapter from 1913 to 1918 and later from 1934 to 1944, when she was elected honorary president for life. On moving to Viborg with her husband, she headed the Society's Viborg chapter from 1928 to 1932.[2]
While Carstensen was involved in improving all aspects of women's rights, she was particularly concerned with the insecurity experienced by married women, given their lack of economic independence. An effect speaker and discussion leader, despite her aristocratic manner she was always ready to take up any aspect of work, including going out on the streets to distribute leaflets or sell the Society's marguerites.[1]
Esther Carstensen died on 12 December 1955 in Copenhagen.[2]