After playing for Shamrock Rovers’ under-18 side at the age of 11, Jennings concentrated on Gaelic football until he was sixteen years old, when he made his soccer comeback with his hometown side Newry Town. After impressing with the team he moved to English Third Division side Watford in May 1963. Jennings again impressed in his first season in England, playing every league game for his club, and making two international appearances that season. He was signed by Tottenham Hotspur for £27,000 in June 1964.

Jennings made his Northern Ireland debut as an eighteen-year-old, whilst playing for Watford. This game, on 15 April 1964, was a British Home Championship match against Wales, Northern Ireland won the game 3–2; George Best made his international debut in the same game. Despite retiring from club football in 1985, Jennings played his final international game at the 1986 World Cup, on his 41st birthday, making him at the time the World Cup’s oldest-ever participant. The match was Northern Ireland’s final group game, a 3–0 defeat against Brazil. In total, Jennings participated in the qualifying stages of six World Cups between 1966 and 1986.

Jennings spent thirteen years at White Hart Lane, where he played in 472 league games for Spurs, and 591 in all competitions. He won the FA Cup in 1967, the League Cup in 1971 and 1973, and the UEFA Cup in 1972. He also scored once, in the 1967 Charity Shield, from his own area, kicking the ball from his hands and sending a large punt down the field that bounced over Manchester United goalkeeper Alex Stepney and into the net. In 1973 the Football Writers’ Association named him as its footballer of the year. Three years later he won PFA’s version of the award – he was the first goalkeeper to receive this accolade, and to this date remains only one of two, along with Peter Shilton.

In August 1977, he was transferred to Tottenham’s arch-rivals, Arsenal, with Tottenham thinking he was nearing the end of his career. However, Jennings saw off rivals for the goalkeeper’s jersey to play for Arsenal for another eight years. Whilst at Highbury, he helped Arsenal to four Cup finals in three successive years; the FA Cup final in 1978, 1979, and 1980, as well as the European Cup Winners Cup final that year. However, Arsenal only managed to win the second of these finals, a 3–2 victory against Manchester United. In total, Jennings made 327 appearances for Arsenal, 237 of them in the League, between 1977 and his eventual retirement from first-team club football in 1985. On 26 February 1983, he became the first player in English football to make 1,000 senior appearances, celebrating this milestone with a clean sheet in a goalless league draw for Arsenal at West Bromwich Albion.

After his retirement, Jennings returned to Tottenham Hotspur, playing mostly in their reserve side to maintain his match sharpness for Northern Ireland’s 1986 World Cup campaign. His final appearance for Tottenham was in the Football League Super Cup against Liverpool in January 1986. He was also briefly on Everton’s books, having been signed as goalkeeping cover for the 1986 FA Cup Final against Liverpool, Neville Southall having been injured playing for Wales.

Following his retirement Jennings has worked as a goalkeeping coach. He has worked at Tottenham in this capacity since 1993. In 2003 Jennings was inducted into the English Football Hall of Fame in recognition of the skills he demonstrated in the English league. His son, also named Pat, is also a goalkeeper, having played for League of Ireland clubs University College Dublin, Derry City, Shamrock Rovers and NIFL Premiership club Glenavon.