A midfielder, Talbot began his footballing career as an apprentice with Ipswich Town in 1968, turning professional in 1972; in the meantime he had spent two seasons on loan with Canadian club Toronto Metros. He made 227 appearances for Ipswich, and won the 1978 FA Cup with the club. In the 1978 FA Cup semi-final against West Bromwich Albion, Talbot scored the first goal eight minutes into the game. He was injured on the play when he collided head-to-head with Albion's skipper, John Wile. Wile played with a bandaged head for the remainder of the contest while Talbot was removed on a stretcher. In January 1979, Talbot moved to Arsenal for a fee of £450,000.
Talbot immediately became a first-team player at Arsenal. He played for the Gunners in the FA Cup final of that year, scoring a goal in a 3–2 victory over Manchester United; Talbot thus achieved the unique distinction of winning the FA Cup with two different teams in consecutive seasons. The following year he set a club record, as an ever-present in Arsenal's marathon 1979–80 season, when he played a total of 70 matches in a single season (the club reached the finals of both the FA Cup and the UEFA Cup Winners' Cup, but lost them both).
Talbot's impressive stamina and fitness meant he played nearly every Arsenal first-team game for the next five seasons, missing fewer than half a dozen League games. In all, the strong and sturdy midfielder played 327 first-team matches for the Gunners, scoring 49 goals. He also played for England, five times while at Ipswich and once as an Arsenal player.
He left Arsenal in June 1985 and joined Watford. He spent a season and a half at Vicarage Road before joining his old Ipswich Town team-mate Mick Mills at Stoke City in October 1986. His presence helped inspire the side as Stoke climbed the table and fell six points short of a play-off place. In 1987–88 made 27 appearances before he left in January 1988 after being offered a player-manager role at West Bromwich Albion. He spent two and a half years in that role before leaving for Fulham in March 1991. After a short spell there he ended his career at Aldershot.
Talbot first tasted football management with West Bromwich Albion, where he served as player-manager from February 1989 to January 1991. His tenure started well, with the side challenging for promotion in the 1988–89 season. But a collapse during the final weeks of the season meant they didn't even achieve playoff qualification. However, the following season saw the side struggle and narrowly survive in the Second Division, which continued into the 1990–91 season. His dismissal from Albion came after the famous 4–2 FA Cup defeat at the hands of non-league Woking. Albion ended the season with relegation to the Third Division for the first time ever. After leaving Albion, he joined Fulham and played five times in the Third Division, scoring once, before being appointed player-manager of Fourth Division strugglers Aldershot, who were deep in debt. After a dismal start to the 1991–92, Talbot left the Shots in November 1991 and was succeeded by Ian McDonald, and four months later the club went bust and were forced out of the Football League. Talbot then moved abroad and managed Maltese club Hibernians, where his team won the island's Premier League in 1993 and 1994.
Talbot returned to English club football as part of the coaching staff of Rushden and Diamonds, then in the Football Conference, in 1997. After a spell as head coach he was appointed club manager before the start of the 1999–2000 season. At the end of the 2000–01 season Rushden secured promotion to the Football League under his management. The team reached the Division Three playoffs in 2002 but lost in the final. In their second season in the League they secured the 2002–03 Division Three title, but were relegated the following season, Talbot having left the club in March 2004 after seven years to take over at Oldham Athletic.
Talbot succeeded in keeping Oldham in Division Two in 2004, then the following season he took them into the 3rd round of the FA Cup where the Latics beat local rivals Manchester City 1–0 thanks to a goal from Scott Vernon. But results in the League were not the same following a defeat to Bolton Wanderers the club went on a 10 match losing streak which led to him resigning at the end of February 2005 following a 5–1 defeat at the hands of Bristol City. In May 2005 he signed a two-year contract as manager of Oxford United before the final game of the 2004–05 season. However, after an unsuccessful stint in charge, Talbot was sacked in March 2006, leaving the club 22nd in League Two and destined to lose their League status at the end of the season.
Talbot made a quick return to management with Maltese side Marsaxlokk, and guided them to the domestic league title and a place in the UEFA Champions League. Following a disappointing start to the 2008–09 season, Marsaxlokk appointed former Msida Saint-Joseph manager Patrick Curmi as the club's new head coach on 17 December 2008. Talbot, however, remained with the club until early 2011, after he took over the Technical Director role. In February 2011, he joined English Premier League side Fulham as a scout. Talbot mostly watches matches in the top leagues for the London club, for example in France or Germany.