Peter was signed from Celtic on August 22nd 1997. A tough, competitive, ball-winning midfielder, Peter is also a skillful passer of the ball. He nearly joined Norwich in 1991/92 for £350,000 but stayed with his first club Celtic for whom he made over 350 appearances. Peter has won full Scottish international honours. He made 37 appearances for Norwich in his first season and was appointed club captain in Matt Jackson's absence through injury.

Peter's name was circulated to Scottish clubs in the spring of 1999 as Norwich seek to rebuild their squad for the 1999/2000 season. He was looking for a coaching position and the Canaries assisted him in his search. His contract at Carrow Road was canceled in July 1999 with one year remaining.

Peter joined Scott Howie, John Polston and Keith Scott at Reading in mid-August 1999 making his debut on 21st August against Luton in a 2-1 home defeat. He made a total of 29 appearances for Reading scoring a solitary league goal

On 3rd May 2000, Ceefax reported that Peter had signed a three year contract with Bournemouth as their player coach effective as of the beginning of the 2000/01 season. Peter made 15 appearances for the Cherries in 2000/01

On 20th January 2004, Alan Pardew, the West Ham manager, parted company with his first team coach Paul Goddard and appointed Peter in his place. The Hammers were promoted to the Premiership through the play-offs in the 2004/5 season, and reached the FA Cup final (and a place in the UEFA Cup) in 2005/6

Peter was linked in early October 2006 with the vacancy at Carrow Road following Nigel Worthington's sacking. The media broke the news that Grant had been appointed as Worthington's replacement on 13th October 2006 although it became official on 16th October 2006. Peter began his managerial career at Norwich well, with the Canaries winning 1-0 at Steve Bruce's Birmingham on 17th October 2006 thanks to a goal from Jason Shackell.

Grant's first season saw the Canaries finish in 16th place. The 2007/8 season started OK but a run of six games within a win or a goal led to him departing the club "by mutual consent" on Tuesday October 8th 2007 following a 1-0 defeat at bottom-placed QPR. Jim Duffy was appointed as caretaker manager. A spokesman for Norwich City said Grant's departure was “by mutual consent” and followed long discussions between the then manager and the board of directors after which Grant said he felt he should step down with immediate effect.

Grant said: “It was a very, very difficult decision for us to make but it was right for myself and the football club going forward. The most important things for me have always been the supporters and the club itself. They are the two constants while managers come and go. Unfortunately for me the balls haven't bounced the right way for me over the last 12 months. I have had fantastic support from the board from minute one right up until the time of leavint but we are in a results-driven business and I don't like being second-best at anything. I would like to thank everyone for the support they have given me through a turbulent 12 months and it goes withous sayting that I wish nothing but success for Norwich City Football Club now and forever.”

After being invited to assist his former Celtic teammate Tony Mowbray with coaching at West Brom, Grant was linked on 4th January 2008 by the Daily Record with the vacant manager's position at Scottish side Hearts. He was not successful.

In early July 2008, Grant was appointed first team coach at West Brom and replaces Craig Shakespeare, who has joined Leicester as assistant manager.