Peter begins to talk about the believers' salvation and faith. Here he elaborates on a metaphor in which what God promises to do for all believers is spoken of as if it were an inheritance that he passes on to them.
Here "new birth" is a metaphor meaning that God has changed the person so that they live their lives in a new way. Here "living hope" is a metaphor meaning an enduring, confident expectation." Alternate translation: "he has caused us to live in a new way, having an enduring, confident hope" (See: [[rc://en/ta/man/translate/figs-metaphor]])