Jennie West was born in Dunedin, New Zealand, on 6 September 1866, the daughter of George Richard West, a music shop proprietor, and his wife, Mary Elizabeth Newman, a music teacher who ran a private school in Moray Place. Jennie had her first music lesson on her fifth birthday. She attended the Normal School and St Dominic's Priory, and had lessons in piano and organ from Arthur Towsey.
The Wests' home was the scene for much music-making. Mary West gave singing lessons and George West conducted and trained local choirs in an annexe to their house; from the age of 10 Jennie accompanied their rehearsals. She made her first public appearance at the age of 11, performing in a piano trio at the Dunedin Glee Club. In 1878 or 1879 she was pianist for the Dunedin Choral Society's season, which included a performance of Mendelssohn's Elijah. A gifted sight-reader, she also played in performances by the touring Simonsen's Opera Company.
In 1881 Jennie West was taken by her father to London to further her musical education. She studied piano with Franklin Taylor, residing with his family and attending a private young ladies' seminary nearby. Taylor's musical circle included the musicologist George Grove, and the composers Arthur Sullivan, C. H. H. Parry, John Stainer and C. V. Stanford, and Jennie attended musical evenings and concerts in this company.
Jennie West returned to Dunedin in 1883. She began teaching music, as a visiting teacher at Otago Girls' High School and later at a private college, and also taught at home. On one occasion when her father was ill she conducted an operatic society rehearsal, to the performers' surprise. She formed a ladies' musical society, which performed works for female voices under her direction. She also appeared in concert as a solo pianist and accompanist, was organist at St Paul's Church from 1886, and later organist and choirmistress at St John's Church, Roslyn. In 1891 she persuaded the Dunedin Choral Society to come out of recess to give a performance of Handel's Messiah, which she would conduct. The concert was a success, despite opposition from some local musicians who were sceptical of a woman's ability to direct a choir and orchestra.
Moving to Christchurch Jennie West formed a ladies' orchestra, taught in schools, and did much accompanying. In 1897 she became organist of St Mary's Church, Merivale, where on 17 May 1900 she married Arthur William Macandrew, a telegraph engineer and amateur singer. They moved to Auckland, Arthur's home, probably soon afterwards; they had no children.
Despite many requests Jennie Macandrew now refused to teach music. She was, however, active in the Parnell and Remuera musical societies, and Auckland choral and orchestral societies. She accompanied singers and instrumentalists, notably the violinist Edith Whitelaw, and performed as a soloist with local orchestras. She was official accompanist to the competitions society in Gisborne for some years from 1913, and toured New Zealand for five months as accompanist to the tenor Philip Newbury. She was also a pianist at Auckland cinemas, and gave radio broadcasts.
In later life Jennie Macandrew continued to perform at the Auckland Society of Musicians' monthly meetings, and she travelled abroad with her husband in 1925 and 1934. After an intensely active and independent musical career, she died at Titirangi on 24 December 1949, two months before her husband's death. Her last public appearance had been a fortnight earlier, at a reception for 'pioneers of music'.