Peter Pett's Commentary on the Bible
Psalms 10 - Introduction
There are indications that this psalm has connections with the previous one. The psalm has no title, the partial acrostic possibly continues, although not consistently, and could therefore easily be a coincidence, while in LXX and the Vulgate they are treated as one psalm. But the possible coincidence of the partial acrostic may in fact have determined the position of the psalm and been responsible for its later being taken as one, rather than vice versa. They are really two separate psalms.
In this psalm the psalmist is puzzled why YHWH does not intervene in difficult times. His cry can be echoed through all ages. He is asking why the unrighteous seem to triumph while the people of God suffer, and describes the unrighteous in great detail, drawing God's attention to what they are.
Then he cries to YHWH to rise up and deal with them, removing unrighteousness, and finally sees ahead to the day when YHWH will indeed be King and the unrighteous nations will be no more. In the end His righteous Kingly Rule will be established for ever.