What does the Bible say about perfection in the new covenant?

According to Hebrews 7:11-19, the Levitical priesthood, established under the old covenant, could not bring about perfection for those who approached God. The sacrifices and rituals were insufficient for true justification and salvation. In contrast, the new covenant, through Jesus Christ—the priest after the order of Melchizedek—provides the perfect and everlasting solution to our sinfulness. Through faith in Him, we are presented faultless before God by His righteousness, as described in Jude 1:24.