Albert Barnes Commentary Psalms 78:10

"They kept not the covenant of God, And refused to walk in his law;" — Psalms 78:10 (ASV)

They did not keep the covenant of God—the covenant which God had made with the entire Hebrew people. They did not maintain their allegiance to Yahweh. Compare Deuteronomy 4:13, Deuteronomy 4:23; Deuteronomy 17:2.

And refused to walk in his law—Refused to obey his law. They rebelled against him.