Stainrod was born in Sheffield and began his career with Sheffield United making his debut towards the end of the 1975–76, he scored twice in seven matches as the Blades suffered relegation to the Second Division. He spent four season at Bramall Lane making 75 appearances scoring 14 goals before he moved to Oldham Athletic in Match 1979. It was at Boundary Park that Stainrod began to make a name for himself scoring 26 goals in 79 appearances which attracted the attentions of Chelsea and Queens Park Rangers. He decided to join Terry Venables' QPR in November 1980 for a fee of £270,000. In the 1981–82 season he was a key player of the team that reached the 1982 FA Cup Final, losing 1–0 to Tottenham Hotspur after a replay, Stainrod scored a career best of 24 goals that season. In 1982–83 he helped the team win the Football League Second Division title and then finish fifth in the First Division qualifying for Europe. After Venables left Loftus Road in 1984 for Barcelona, the side quickly fell apart under the unsuccessful reign of Alan Mullery and many players including Stainrod left the club. Stainrod then had an unsuccessful spell at Sheffield Wednesday, and was sold to Aston Villa for £350,000 in September 1985 and he enjoyed a spectacular debut when he scored all four goals against Exeter City in the League Cup. Despite scoring 21 goals for Villa in 1985–86 he struggled to get in the team in 1986–87 and the team were relegated to the Second Division. In January 1988 he joined Mick Mills' Stoke City where he scored twice in 16 appearances in 1987–88. In 1988–89 Stainrod score five goals in 18 appearances before moving to France. He spent the 1988–89 season in France with RC Strasbourg. He then spent a further spell with FC Rouen before moving to Scotland to play for Falkirk and Ayr United and then managing Dundee in Scotland. During Stainrod's spell at Falkirk he famously scored from the halfway line against St Johnstone direct from a kick off.
Post playing career
He is also a FIFA-licensed football agent and is now based in Cannes, France. In 2003, he set up his own company with a couple of his friends called Matchday Media. Stainrod was working with Hatem Ben Arfa following his move to Newcastle United as his adviser.