Paul on the Last Supper
For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, “This is my body which is for you. Do this in remembrance of me.” In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.” For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes. 1 Cor 11:23-26 (ESV)
See Matthew 26; Mark 14; Luke 22.
Paul Paralleling Jesus in Matthew 5:32 on Divorce
To the married I give this charge (not I, but the Lord): the wife should not separate from her husband (but if she does, she should remain unmarried or else be reconciled to her husband), and the husband should not divorce his wife. 1 Cor 7:10-11 (ESV)
Paul Paralleling Jesus in Matthew 10
In the same way, the Lord commanded that those who proclaim the gospel should get their living by the gospel.
1 Cor 9:14 (ESV)
More Clear Allusions
Even when Paul ins't quoting Jesus, he is well acquainted with the sayings of Jesus during his earthly ministry. For example, Romans 12:1-15:7 draws on the Sermon on the Mount; When Paul speaks of “the meekness and gentleness of Christ” (2 Cor. 10:1), we can see Jesus said of himself in Matthew 11:29, “I am meek and lowly in heart”; The self-denying Christ of the Gospels is the one of whom Paul says, “Christ did not please himself” (Rom. 15:3); and just as the Christ of the Gospels called on His followers to deny themselves (Mark 8:34), so the apostle insists that, after the example of Christ, it is our Christian duty “to bear the infirmities of the weak, and not to please ourselves” (Rom. 15:1)"
If we want to ask ourselves why Paul did not spend time retelling the Gospels - why would he? The communities he was writing to would have already had access to the gospel narrative as well as Jesus sayings.
Marcus Borg states:
"But Paul’s letters tell us very little about the life and message of Jesus. This does not mean that Jesus’s historical life was unimportant to Paul, as some scholars have suggested. Rather, Jesus mattered greatly to Paul. Paul spoke of Jesus as Lord and as God’s Son, as did early Christians generally. He wrote about life “in Christ,” “Christ crucified,” and “imitating Christ.” But narrating the story of Jesus was not the purpose of his letters. Rather, as the literary genre of “letters” indicates, Paul was writing to Christian communities about issues that had arisen in their life together." (Marcus Borg, Jesus p.32)