An offering was made by a high priest as a means for the sinner to be redeemed. Christ is for us sinners both the high priest and the offering that is sacrificed.
We Christians can read this as reassuring.
We should be grateful but not triumphalistic.
Further, we should be careful not to misinterpret the phrase, "dead works."
According to Allen & Williamson's Preaching the Letters without Dismissing the Law
The "dead works" should not be confused with the mitzvoth of torah. "Dead works" are not "deeds of loving kindness"; they are sins that pollute the conscience.