Clemence joined Liverpool in June 1967 from Scunthorpe United for a fee of £18,000, he made his debut and kept his first clean-sheet in a League Cup 3rd round tie at Anfield on the 25 September 1968, Swansea City were the visitors and were beaten 2-0. He was nurtured through the reserve side over the next two years, with the occasional senior appearance, until 1970, at which point he became the club's first choice goalkeeper.
In 1971, Liverpool reached the FA Cup final where Clemence played well but was powerless to prevent Arsenal scoring twice in extra time to peg back Liverpool's lead and win the game 2–1. However, there would be joy for Clemence two seasons later when Liverpool won both the League title and UEFA Cup, with Clemence saving a penalty in the final of the latter against Borussia Mönchengladbach. The penalty save meant that Liverpool took a 3–0 lead to Germany with them rather than a 3–1, Gladbach won 2–0 on their home soil and if Jupp Heynckes had beaten Clem from the spot the tie would have finished 3–3 on aggregate with the Germans winning on the away goals rule. 1973/74 saw Liverpool claim yet more silverware winning the F.A Cup at a canter with a comprehensive 3–0 victory over Newcastle United.
Clemence was, by now, a regular for England making his debut and keeping his first clean-sheet in the 1–0 World Cup qualifier win over Wales at Ninian Park on the 15 November 1972, unfortunately for Clemence the presence of another great goalkeeper Peter Shilton meant that the England management struggled to decide which keeper was the best, and ended up alternating their selection.
With Clemence in goal, Liverpool won another League and UEFA Cup double in 1976 and then made a courageous bid for a unique treble a year later. They achieved the first leg when they won the League title, but then lost the F.A Cup final to bitter rivals Manchester United, a result that affected Clem and saw him trudge forlornly off the Wembley turf. A consolation was to be had a few days later, however, when the Reds won the European Cup for the first time, defeating Borussia Mönchengladbach 3–1, with Clemence, again, being a thorn in the Gladbach side making a series of important saves.
Liverpool retained the European Cup in 1978 with a narrow 1–0 win over Club Brugge at Wembley, but conceded their League title to Nottingham Forest, to whom they also lost in the League Cup final. In 1979 and 1980, Clemence kept goal as Liverpool clinched the League title in each season. The 1978-79 League success saw Clemence set a record that was never beaten under the two points for a win system, conceding only 16 goals in the 42 league matches ( and just 4 at Anfield). This remarkable record endured until beaten recently by Chelsea, who conceded 15 goals in the 38 League matches.
Once again in 1981 silverware proudly sat in the Anfield trophy room as they won the League Cup and the European Cup for the third time, the 1–0 win over Real Madrid at the Parc des Princes on the 27 May ultimately proving to be Clemence's last game for the club. The emergence of the South African-born Bruce Grobbelaar put Clemence under threat for his place for the first time in eleven years (during which period he played in more than 650 matches and missed a mere six) and he decided Leave Liverpool by joining Tottenham Hotspur for a fee of £300,000.