Here the word "letter" means letters of the alphabet and refers to words that people write down. The phrase alludes to the Old Testament law. Alternate translation: "a covenant not based on commands that men have written" (See: [[rc://en/ta/man/translate/figs-synecdoche]] and [[rc://en/ta/man/translate/figs-explicit]])
The Holy Spirit is the one who establishes God's covenant with people. Alternate translation: "but a covenant based on what the Spirit does" (See: [[rc://en/ta/man/translate/figs-ellipsis]])
Paul speaks of the Old Testament law as a person who kills. Following that law leads to spiritual death. Alternate translation: "the written law leads to death" (See: [[rc://en/ta/man/translate/figs-personification]] and [[rc://en/ta/man/translate/figs-explicit]])