[5] In March 2002, Norris joined Football League Third Division club Hull City on loan, where he played in six matches and scored once.
[8] He scored the decisive goal on his debut in a 1–0 win at Crewe Alexandra,[9] and made seven league appearances before joining the club permanently for an undisclosed fee in December.
[10][11] Argyle won promotion to the EFL Championship as Second Division champions in 2004 with Norris scoring five goals in 45 league appearances that season.
In November 2008, Norris was heavily criticised for a controversial goal celebration against Blackpool, interpreted as a show of support for jailed friend and former Plymouth goalkeeper Luke McCormick.
[12] McCormick was returning from Norris' wedding in June 2008 when he fell asleep at the wheel due to the effects of alcohol and caused the deaths of two young boys.
[14] He was once again caught out when he told the Ipswich website[15] he had not intended the celebration as a show of support to Luke McCormick and the statement was later changed by the club, adding further to the controversy.
Later that week it was revealed that Norris was fined £25,000 by Ipswich and would make a face-to-face apology to Phil and Amanda Peak (the parents of the two boys).
With the match goalless, Karim Rekik headed the ball down to Norris, who controlled and then volleyed it into the net from the edge of the penalty area.
[31] Norris missed the final three games of the season under new manager Brian McDermott due to a knee injury that required surgery,[32] and on 15 August 2013, with Leeds needing to raise finances to help fund signings, he was made available for transfer alongside teammates El Hadji Diouf and Adam Drury.
[36][37][38] Norris made his first appearance for Leeds in over a year in the last game of Head Coach Dave Hockaday against Bradford City in the League Cup, providing an assist for striker Matt Smith who opened the scoring in a 2–1 defeat on 27 August 2014.
On 21 August 2015, Norris signed for League Two side Yeovil Town on non-contract terms, linking up with his former Plymouth manager Paul Sturrock.
At the start of the 24/25 season, David signed for Peterborough & District Football League Division One side, Whaplode Drove Rovers.