“The insolent utterly deride me, but I do not turn away from your law.”
Insolent is referring to the proud. Obviously, we all are proud, but the Psalmist here is talking about those who mock God, and make a jest of the gospel. As Christians, we’ve all experienced this at some point, and maybe this was how we were before God rescued us.
The point in this verse is that he doesn’t let the insolent discourage him from following the Lord. He is not afraid of what God’s law says, and is also not discouraged from obeying it. When we fear people more than God, then their approval will be more important. But, when God is big and people are small, we’ll be freed up to worship the Lord and worry less about the approval of people.