Born in Bramford, Suffolk, England, on 3 November 1832, Elizabeth Mary Naylor came from a family of landed gentry with close connections to the Anglican church. Her father, George Naylor, was successively vicar of Bramford-cum-Burstall and Rougham in Suffolk; her paternal grandfather was a prebendary of Canterbury cathedral and headmaster of King's School, Canterbury. Her mother was Elizabeth Caroline Smith.
Little is known of her early life, but she clearly received an excellent grounding in music, attaining a technical skill unusual for an amateur. On 31 May 1853, at London, she married a farmer's son, George Palmer. Three years later, accompanied by one of her brothers and his family, she, her husband and a daughter sailed for Nelson, New Zealand, arriving on the schooner Cresswell on 6 October 1856. A son was born during the voyage.
The births of a further seven boys and four girls are recorded over the succeeding years, two dying in infancy. George Palmer found work mainly as a gardener or nurseryman. Financial necessity may have led Elizabeth Palmer to begin exploiting her musical talents professionally once her older children were able to help run the household. From 1871 she advertised as a teacher of music and singing from the family home in Waimea Street. She also began a career as a performer, and a promoter of theatrical events.
In Nelson she organised musical evenings and dramatic entertainments with predominantly amateur casts. The latter, which characteristically featured a melodrama followed by assorted musical items and an amusing farce, proved particularly popular. A year or two later, joining forces with a resident Swedish-born violinist, Andrew Norberg, she added regular concerts in Picton and Blenheim to her schedule. Her daughter Alice, an accomplished singer and pianist by her late teens, usually took part in these, while Emily was an occasional participant. The programmes comprised ballads, piano variations on favourite airs, and operatic excerpts and arrangements. The frequency with which 'Mrs Palmer and Herr Norberg' presented their 'Popular Concerts', and the complimentary and appreciative reviews which greeted them, showed that they fulfilled a real need for public entertainment in the Marlborough area.
By 1876 Elizabeth Palmer was giving concerts in Wellington, and she may briefly have taken up residence there. By 1878, however, the Palmer family had settled in Wairarapa, where Elizabeth continued her musical career. She gave concerts in Masterton, taught at Clareville School and continued to advertise as a private singing teacher. Unusually for a woman of the period, she was listed as a freeholder in Clareville.
Her only known composition, a drawing-room ballad "Twas only a dream', for which she wrote both words and music, was published about 1884 and received favourable notice. Around the same time the Palmers moved to Wellington, which provided a larger stage for Elizabeth to display her talents. She remained active as a teacher and performer, and her concerts now featured such prominent musical figures as the tenor E. J. Hill and baritone John Prouse. In 1889, while visiting one of her married daughters, she made highly successful concert appearances in Dunedin.
During the early 1890s Elizabeth Palmer's performing activities gradually ceased. She suffered from ill health, and her diary from this time reflects her strong religious faith in adversity. In 1895 the Palmers' fourth son, Herbert, was killed in a shooting accident in the Orongorongo valley. George Palmer died on 30 April the following year, and Elizabeth did not long survive these twin blows. She died at the family home in Marion Street, Wellington, on 31 May 1897.