Hebrews 9:15

For this cause; in view of what has just been said of the superior efficacy of his priesthood.

The new testament; the words "covenant" and "testament" are, in the original, the same. The new covenant, of which Christ is the Mediator, is also a testament when considered as ratified and made valid by his expiatory death on the cross.

For the redemption of the transgressions; for their forgiveness through the payment of a ransom. The power of Christ's expiatory sacrifice extends backward to the beginning of the world, as it does forward to its end.

They which are called; the called of God of all ages, before and after Christ's advent.