John Gill Commentary Psalms 9:4

"For thou hast maintained my right and my cause; Thou sittest in the throne judging righteously." — Psalms 9:4 (ASV)

For you have maintained my right and my cause
Or vindicated and established his righteous cause; God had pleaded and defended it, and by the flight, fall, and ruin of his enemies, had clearly made it appear that his cause was just and good;

you sit in the throne judging right ;
God has not only a throne of grace on which he sits, and from where he distributes grace and mercy to his people, but he has a throne of judgment, which is prepared for it, as in (Psalms 9:7); where he sits as the Judge of all the earth, and will do right; nor can he do otherwise, though his judgments are not always manifest in the present state of things.

And the vindication of the psalmist's innocence and uprightness is another reason of his joy and gladness.