Palmer studied composition at the Royal Academy of Music with Richard Rodney Bennett, winning the Eric Coates Prize and The Boosey and Hawkes Prize. She was appointed a Fellow of The Royal Academy of Music in 1994.
Going about her early career as a jobbing arranger and conductor of recording sessions, Palmer recorded her first album project, Nicola, in 1967 with Bert Jansch. She was then referred to Terry Ellis, then manager of the early Jethro Tull, which was making its first album at Sound Techniques Studio in Chelsea, London. At short notice, Palmer came up with arrangements for the horns and strings on the Mick Abrahams composition, "Move on Alone" from the This Was album. This work and professional performance endeared her to the band and she was soon to visit them again, with a string quartet arrangement to "A Christmas Song". Palmer arranged string, brass, and woodwind parts for Jethro Tull songs in the late 1960s and early 1970s, before formally joining the group in 1976 and primarily playing electronic keyboard instruments. In 1980, leader Ian Anderson intended to release the album A with other musicians as a solo project (under the name 'Ian Anderson') but was persuaded by his record label to release it instead under the 'Jethro Tull' name. This resulted in every member of the group, including Palmer, leaving except guitarist Martin Barre and Anderson himself. Palmer formed a new group, Tallis, with former Jethro Tull pianist and organist John Evan. The new group was not commercially successful, and Palmer returned to film scoring and sessions.
In 2003, Palmer came out as transsexual and intersex, changing her name to Dee. Palmer was born with genital ambiguity, assigned female at birth, and underwent several surgeries, the last in her late twenties. Palmer said her gender dysphoria had been a part of her life since she'd been young, and that the dysphoria "started to reassert itself again" in the year following the death of her wife Maggie in 1995.