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. After a year in the Premiership, Mowbray, despite relegation, was appoitned manager at Celtic and took Grant with him.

Mowbray and Grant were sacked by Celtic on 25th March 2010 followCeltic's 4-0 loss to St Mirren in the Scottish Cup; it didn't help that the Hoops were lagging behind Rangers in the Scottish Premier League.

On 15th July 2010, Grant signed as first-team coach for Birmingham City replacing Roy Aitken, who last week left the Barclays Premier League club to link up with David O'Leary at United Arab Emirates outfit Al Ahli. Blues boss Alex McLeish told the club's website: “I've known Peter for a long time. He was an adversary of mine in my Aberdeen playing days, when he was a stalwart for Celtic. He is a competitive man who has been brought up in a winner's environment due to the traditions of Celtic. He has successfully made the transition into becoming a coach and my diligence shows me he is the right man for the job."

After Alan Pardew was appointed manager of Newcastle in December 2010, he approached Grant to become his number 2 at St James’ Park but Grant rejected the approach choosing to stay at Birmingham. In fact, former Newcastle manager Chris Hughton had approached the highly rated Grant to work for him. Grant had been a player at Reading under Pardew briefly and four years later, out of the blue, got a call asking if he would assist at West Ham. Grant was at Bournemouth at the time. Under Pardew’s guidance with Grant at his side, West Ham won the Championship play-offs, reached the 2006 FA Cup final, losing to a Steven Gerrard-inspired Liverpool on penalties, and finished ninth in the Premier League.

In his first season with Birmingham, the Blues won the League Cup beating Arsenal 2-1 at Wembley on 27th February 2011. However Grant and Birmingham were relegated to the Championship on 22nd May 2011, following a 2-1 defeat at Spurs.

Grant followed McLeish to Villa Park in the summer of 2011 becoming Assistant Manager. They were sacked on 14th May 2012 after Villa narrowly escaped relegation to the Championship.

Grant teamed up again with McLeish when he was named McLeish's deputy manager at Notts Forest on 2nd January 2013. However by 6th February 2013, Grant had left the club mere days after McLeish had departed after falling out with Forest's Kuwaiti owners.