Hindmarsh was born in Leeds and educated at Lawnswood High School. There, she was prominent in the school's musical and theatrical productions, including Merrie England in 1950, in which she played Sir Walter Raleigh. Hindmarsh gained her teaching diploma (ARMCM) from the Royal College of Music in Manchester and then continued to study opera for an additional 18 months. She played the lead in two college productions and sang in concerts and oratorios. Hindmarsh was the runner-up in the first Kathleen Ferrier Competition in 1955 and won the Blackpool heat against 97 competitors. A representative from the D'Oyly Carte Opera Company heard her performance and invited her to audition.
Hindmarsh was engaged by the D'Oyly Carte Opera Company in March 1956 as principal soprano. Over the next four years, she played the title role in Princess Ida, Mabel in The Pirates of Penzance, Elsie Maynard in The Yeomen of the Guard, Gianetta in The Gondoliers and Josephine in HMS Pinafore, soon adding the small role of Lady Ella in Patience. In 1959, she began instead to play the title role in Patience. Hindmarsh married in 1960 and left the D'Oyly Carte organisation when she was expecting her first child. She rejoined the Company as a guest artist in her old roles for seasons in 1961–62, 1962–63, in the spring of 1963, 1963–64, and in the spring of 1969. These included two London seasons, one provincial tour and one American tour. In reviewing Princess Ida in 1961, The Times wrote that, in the title role, "Hindmarsh charms, amuses and... moves the audience". That paper commented on a 1962 performance of The Gondoliers: "Outstanding among last night's cast was Miss Jean Hindmarsh, a winning Giannetta both in appearance and voice."
Hindmarsh sings the lead soprano roles on four D'Oyly Carte recordings: Yum-Yum in The Mikado (1957), Mabel in Pirates (1957), Josephine in Pinafore (1960), and Rose Maybud in Ruddigore (1962), even though she never played Yum-Yum or Rose with the company. Of the 1957 Pirates, reviewer Mel Moratti wrote, "The highlights must be the pairing of Thomas Round and Jean Hindmarsh as Frederic and Mabel. Their solos and duets are most delightful". The Rough Guide to Opera comments that she "is a uniquely charming Josephine" in Pinafore.
In recent years, Hindmarsh has performed and given talks at the International Gilbert and Sullivan Festival. At the Festival, in 1999, Hindmarsh and baritone Michael Rayner gave the world premiere performance of "Reflect, my child", a song cut from H.M.S. Pinafore before the opera opened in 1878 and reconstructed in 1998.
- Famous Old Girls Lawnswood High School Alumnae Website, accessed 4 November 2008
- Cottier, M. N. Merrie England review, Lawnswood High School Magazine, 1950, accessed 4 November 2008
- Ayre, p. 144
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- Stone, David. Jean Hindmarsh at the Who's Who in the D'Oyly Carte Opera Company website, 2002, accessed 4 November 2008
- Taylor, Roy. Profile of Jean Hindmarsh at the Memories of the D'Oyly Carte website, accessed 4 November 2008
- "Anti-Romantic Work Rich in Romance", The Times, 28 December 1961, p. 12, col. D
- "The Gilbert and Sullivan Cycle Completed", The Times, 16 January 1962, p. 5, col. F
- Shepherd, Marc. "The 1957 D'Oyly Carte Mikado", A Gilbert and Sullivan Discography, 2005, accessed 4 November 2008
- Shepherd, Marc. "The 1960 D'Oyly Pinafore", A Gilbert and Sullivan Discography, 2003, accessed 4 November 2008
- Shepherd, Marc. "The 1962 D'Oyly Carte Ruddigore", A Gilbert and Sullivan Discography, 2003, accessed 4 November 2008
- Shepherd, Marc, quoting Moratti. "The 1957 D'Oyly Carte Pirates", A Gilbert and Sullivan Discography, 2003, accessed 4 November 2008
- Boyden et al., p. 318
- Bourke, Kevin. "Music festivals 2004: Buxton Gilbert & Sullivan Festival", Manchester Evening News, 29 July 2004, accessed 4 November 2008
- Marshall, Trevor. "Ian Smith's 'Stars on Sunday'", 1998, accessed 4 November 2008
- "Gilbert & Sullivan Rarities: Music from the Cutting-Room Floor", Festival review, Day 2: 29 July 1999, accessed 4 November 2008
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- Ayre, Leslie (1972). The Gilbert & Sullivan Companion. London: W.H. Allen & Co Ltd. Introduction by Martyn Green.
- Boyden, Matthew, Nick Kimberley and Joe Staines. The Rough Guide to Opera, Rough Guides, 2002 ISBN 1-85828-749-9