And accordingly...
And accordingly, the meaning of the verse is this: We wrote in Psalms adding to holy Qur’an (of after Torah) that my competent and righteous servants will have the earth; and it is enough for the group of worshipers (and those who make their steps in the way of servitude of god) in order to reach their goals. Mentioning this matter in “زبور” (if it means all previous divine books) is the reason for this matter to be available in all divine books as a constant principle.
And if the purpose of that is Psalms of David then maybe it is because David had an expanded kingdom which was in the way of truth, justice and human interests; although it was regional and not comprehensive to the entire world; but it was announced to him in Psalms that a comprehensive universal government, based on freedom, security and justice, is waiting for the people of the world.
It means that when they become enough competent and become the living example of “عبادی الصّالحون” and righteous servants of God, they will inherit and gain all the heritages and gifts of the earth, both material and spiritual governments. More explicit and clearer expressions can be found in some narratives, which have been quoted in interpretation of above verses.
For instance, it is quoted in famous interpretation of “Majma’ al-Bayan” from Imam Baqir (as) beneath the above verse that: هم اصحاب المهدی فی آخر الزّمان These are the companions of Mahdi (as) in End of Days. Those self-constituted persons men and women who will inherit all the heritages of the earth; and will have the competence of this great prophecy.
It is interesting that, the same exact matter can be found, with different expressions, in “Psalms of David”, which is today included in the Old Testament: For instance, we read in psalm 37: 9 For the wicked shall be cut off; but those who wait for the Lord shall possess the land. 10 Yet a little while, and the wicked will be no more; though you look well at his place, he will not be there. 11 But the meek shall possess the land, and delight themselves in abundant prosperity.
Also, in psalm 37, this matter is mentioned with different expressions: 22 for those “blessed” by the Lord shall possess the land, but those cursed by him shall be cut off. 29 The righteous shall possess the land, and dwell upon it forever.