Moore was already active in the Birminghamrock, blues, folk and country scene, and played with numerous bands, including The Young Casuals, The Other Lot, The Outer Light, Gabriel Oak, Glad Stallion, Tendency Jones and Pendulum. He was first approached by guitarist K. K. Downing and bassist Ian Hill in 1971, and joined in the early and unofficial phase of the newborn Judas Priest for a period of about a year (during this time Al Atkins was still the vocalist). He left in 1972 to join the Birmingham country rock band, Sundance, with whom he recorded the album Rain, Steam, Speed (1974), and their single, "Coming Down".
In 1975, drummer John Hinch left Judas Priest, and Downing and Hill re-approached Moore. For the second time, Moore joined the band, making him the only drummer in the history of Judas Priest to have two separate stints. His first show after re-joining was in 1975.10.11 - Slough College, London, UK, during which guitarist/backing vocalist Glenn Tipton introduced "our new drummer Skip" who "only had a few hours of rehearsal". In 1976, they recorded the album Sad Wings of Destiny. Despite the success of the album, Moore decided to leave again, only this time permanently.
Moore continued to play with other bands, including Zenda Jacks Stormbringer and others. In 1981 he signed to Ariola Records with the band R.P.M., releasing two singles; Now That Summer's Here and Lost In Space. Eventually, he retired from music and worked as a truck driver, disappearing into anonymity. In fact, he drove trucks for Edwin Shirley Trucking from 1978 until the late '80's when he decided to call it a day and make a living building high quality bespoke kitchens, something which he continues to do. He recently moved with his wife and two sons to live on The Isle of Wight. Several musical biographers, journalists, band members, and fans have tried to trace Moore without success. In the official biography The Story Of Judas Priest: Defenders Of The Faith, author Neil Daniels said that Moore was the only former member of the band he could not trace at all.