On 6 April 2021, Tavernier signed a new three-year contract. He made his 300th Rangers appearance on 25 September in a 1–0 win at Dundee, having 66 goals by that point. In February 2022, he scored a penalty to open a 4–2 win at Borussia Dortmund in the last 32 of the Europa League, and scored both Rangers goals in a draw in the second leg to advance. He netted another brace on 14 April, as the team won 3–1 at home to Braga after extra time to make the semi-finals, where he scored against RB Leipzig. He was the top scorer with seven goals as the team finished runners-up to Eintracht Frankfurt and netted Rangers' first attempt in the penalty shootout loss in the final. He was the first defender to be top scorer in a European season since Ronald Koeman for FC Barcelona in the 1993–94 UEFA Champions League.
