Isaiah 9:7 Of the increase of his government and of peace there shall be no end, on David’s throne, and on his kingdom, to establish it, and to uphold it with justice and with righteousness from that time on, even forever. The zeal of the Lord of Armies will perform this.

Isaiah 11:1 A shoot will come out of the stock of Jesse [David’s father], and a branch out of his roots will bear fruit.

Jeremiah 23:5 Behold, the days come, says the Lord, that I will raise to David a righteous Branch, and he shall reign as king and deal wisely, and shall execute justice and righteousness in the land.

Ezekiel 34:23-24 I will set up one shepherd over them, and he shall feed them, even my servant David; he shall feed them, and he shall be their shepherd. I, the Lord, will be their God, and my servant David prince among them; I, the Lord, have spoken it.

This was the common understanding of Jews in Jesus’ Day:

Luke 1:69-70 and has raised up a horn of salvation for us in the house of his servant David (as he spoke by the mouth of his holy prophets who have been from of old)

Matthew 22:42 saying, “What do you think of the Christ? Whose son is he?” They said to him, “Of David [i.e. descendant of].”