What does the Bible say about the covenants in relation to salvation?

In scripture, particularly in Galatians 4, we see two covenants represented by two mothers: Hagar, a slave, who represents the Old Covenant of the law, and Sarah, a free woman, who represents the New Covenant of grace. The Old Covenant, established at Mount Sinai, entails obeying God's law to gain acceptance. In contrast, the New Covenant is rooted in God's promises, accomplished through Christ, who fulfills the law for us and grants us freedom from sin and assurance of salvation through faith. This is critically important as it emphasizes that salvation is not based on our works but on God's sovereign grace and promises in Christ.