His career started at Aberdeen, helping the Dons to finish second in the Scottish Premier League in the 1993–94 season. Whilst at the top of his game for Aberdeen, he was connected with moves to the likes of Parma, at the time flying high in the Italian Serie A. In 1996, he earned a move to Coventry City but this lasted just over a year, during which he scored just once against QPR in 39 Premier League games and scored an own goal in a game against Manchester United. He did however score twice in Coventry's run in the 1996/97 FA Cup in games against Woking and Blackburn Rovers. He then returned to Aberdeen for a second spell.
He returned to the Premier League with Bradford City in 2000 but despite finishing the season as top scorer, financial problems meant he was released in 2002 following the collapse of ITV Digital. He joined Nottingham Forest in August 2002 and in his first season steered Forest into the play-offs. However they were relegated in 2005 and Jess moved on as a free agent. In July 2005 he signed for Northampton Town, and was released from his contract there on 11 April 2007. He later rejoined Nottingham Forest as a coach for the youth team a job he left in May 2012.
In April 2009, at the age of 38, Jess suffered a mild stroke.