In the 1982 season, Moir played regularly for Derbyshire first team, where he stayed for three years.
He finished playing for Derbyshire at the end of 1985 but represented Scotland again in 1986, his first-class match being in an innings victory against Ireland.
Moir was a right-handed batsman and played 87 innings in 73 first-class matches with an average of 15.42 and a top score of 107.
He was a slow left-arm bowler and took 206 first-class wickets with an average of 32.98 and a best performance of 6 for 60.
Moir's twin brother, Jeremy, played first-class and List A cricket for Scotland in the NatWest Trophy and the Benson and Hedges Cup between 1989 and 1992.