The risen Jesus tells the disciples that what was written about him in 'the law of Moses, and in the prophets, and in the psalms' must be fulfilled. He then opens their understanding of the Scriptures.
The wording places Christian interpretation of Jesus squarely within Israel's sacred writings.
Jewish Scripture was commonly understood in major groupings, especially Torah or Law and the Prophets, with additional sacred writings. Luke's mention of 'Psalms' may represent the Psalter specifically or function prominently within the wider collection later known as the Writings. It should not be forced into a claim about every detail of a later fixed canonical arrangement.
Luke has already shown Jesus interpreting Moses and the Prophets on the Emmaus road.
The scriptural framework matters because the disciples' problem is not simply lack of information about recent events. They must learn to see suffering, resurrection, and mission within the story told by Israel's Scriptures.
Luke therefore ends his Gospel not by leaving the Old Testament behind, but by presenting the risen Jesus as the one who opens its meaning to his followers.