"For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance" (Hebrews 9:15).
You requested any scripture concerning "redemption and hope." There are dozens of possibilities, from which I've chosen this statement from the Letter to the Hebrews. We understand "He" to be the Christ—the eternal spiritual Truth, which Jesus brought into human manifestation.
The "first covenant" was the Law established through the ministry of Moses; this is essential so long as the Truth—the Christ—remains a matter of blind faith. Now Jesus has removed our blinders, so to speak, to show us our own true identity as the Christ. It is that knowledge, and the new choices that become possible, that constitutes our "redemption." So, it's a matter of having faith in the Christ—as it expresses through Jesus and as it can now express through us thanks to his example.