The writer of Hebrews provides one of the most stark expressions of the contrast between the covenant of law and the covenant of God's grace and truth in the Lord Jesus Christ.
"We are sanctified through the offering of the body of Jesus Christ once for all. And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins: but this Man, after He had offered one sacrifice for sins for ever, sat down on the right hand of God; from henceforth expecting till His enemies be made His footstool. For by one offering He hath perfected for ever them that are sanctified" (Hebrews 10:10-14).
The blood of bulls and goats offered by the Old Testament priests did not take away sins, but rather foreshadowed the blood of the Lord Jesus Christ that perfectly succeeded in justifying those who believe. God the Father was not satisfied by Levitical offerings for sin, but He was so pleased and appeased by the offering of the Lord Jesus that His Son could sit down at His right hand. And the priests of old offered many sacrifices that "can never take away sins." Our great High Priest "offered one sacrifice for sins forever," and then sat down from a work so complete that "by one offering He hath perfected forever them that that are sanctified."
Failure to understand the qualitative and quantitative difference between law and grace leads to much confusion, and much weakness in "bearing the fruits of righteousness which are by Jesus Christ" (Philippians 1:11). Mixing the two covenants, a common error, results in the power of God's grace in the Lord Jesus being diluted both in our joyful apprehension, and in the practical enabling that results from knowing how near God has drawn us to Himself in Christ.
The law focuses our attention primarily on our doings - "the man that doeth them (the works of the law) shall live in them" (Galatians 3:12). Grace directs our gaze to the blessed "looking unto Jesus, the author and finisher of our faith" - "we are His workmanship, created in Christ Jesus unto good works" (Hebrews 12:2; Ephesians 2:10). We either attempt to live from the root of our fallen humanity, or from the dynamic source of the crucified and risen Christ who is "the power of God unto salvation" (Romans 1:16). "The law could not do" declared the Apostle Paul (Romans 8:3). Conversely, "God is able to make all grace abound toward you; that ye, always having all sufficiency in all things, may abound to every good work" (II Corinthians 9:8). The choice is clear, and the best course obvious. May we thus "grow in grace, and in the knowledge of our Lord and Savior Jesus Christ" (II Peter 3:18).
"The letter killeth, but the Spirit giveth life."
(II Corinthians 3:6)