The phrase "your life" refers to "you," but it emphasizes that Yahweh gives blessings throughout life. Alternate translation: "He satisfies you with good things through your life" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Having your "youth renewed" means to feel young again. Here David compares this feeling of youth to the swiftness and strength of an eagle. Alternate translation: "you feel young and are strong like an eagle" (See: [[rc://en/ta/man/translate/figs-simile]])