Psalm 130 is known as a Pauline psalm because it speaks to the grace and mercy of God. This was a theme Paul wrote on extensively.
For all have sinned and fall short of the glory of God. 24 They are justified freely by His grace through the redemption that is in Christ Jesus.
Romans 3:23-24 HCSB
In the same way, then, there is also at the present time a remnant chosen by grace. 6 Now if by grace, then it is not by works; otherwise grace ceases to be grace.
Romans 11:5-6 HCSB
But by God’s grace I am what I am, and His grace toward me was not ineffective. However, I worked more than any of them, yet not I, but God’s grace that was with me.
1 Corinthians 15:10 HCSB
It’s interesting to consider that these OT writings would contain the fullness of grace and mercy that was yet to come in Jesus Christ. With the law of Moses drilled into their minds, the readers of this psalm may have wondered what it means to wait on the Lord and receive full redemption of their sins.
Israel, put your hope in the LORD. For there is faithful love with the LORD, and with Him is redemption in abundance. 8 And He will redeem Israel from all its sins.
Psalms 130:7-8 HCSB
Israel put their hope in the Lord. Jesus both claimed to be God and demonstrated God’s power in the flesh. He is the fulfillment of this command to wait and trust that their sins will be redeemed.