The key to this question is found in Isa 55:3 -
Incline your ear and come to Me; listen, so that your soul may live. I
will make with you an everlasting covenant— My loving devotion [חֵסֵד =
loving kindness, goodness, devotion etc] promised to David.
The LORD's covenant with David, also known as the royal or Davidic covenant is spelled out in several places, see appendix below. This covenant was an everlasting or eternal covenant (Isa 55:3); but from an earthly point of view, it failed because David's dynasty and throne ended with the Babylonian capture in the 6th cent BC.
However, Jesus says in Matt 5:17-19 that he came to fulfill the OT law (= covenants, etc) which the NT is at pains to point out. In the case of the Davidic covenant, Jesus became the eternal king and the eternal throne and thus fulfilled the Davidic promises. See appendix below.
The important fact, which Paul uses in Acts 13:34 is Jesus' indestructibility because He was resurrected, and thus Jesus can be called the eternal king that inherits the blessings of the eternal Davidic covenant.
APPENDIX - Davidic Covenant
The Davidic (or Regal, or Royal) Covenant: 2 Sam 7, 23:5, 1 Kings 6:11, 12, 8:25, 1 Chron 17:11-14, 2 Chron 6:14-16, 7:17, 18, 13:5, Ps 89:4, 29, 34, 39, 132:11, 12, Jer 33:21, Eze 37:15-28. This is an eternal covenant. The provisions of the Davidic Covenant were as follows.
- God promised to make David, a shepherd king over Israel. 2 Sam 7:9, 1 Kings 8:25, 2 Chron 21:7.
- God promised to defeat all David’s enemies and give him peace on all sides, 2 Sam 7:9
- David’s name would be great, 2 Sam 7:9-11
- God promised there would always be a blood descendant of David on his throne, by an eternal “covenant of salt” (ie very solemn), 2 Chron 13:5, forever, 2 Sam 7:13, 15, 16, Eze 37:26, (2 Sam 23:5).
- God promised that the descendant of David would have God as his Father and he would be His son, 2 Sam 7:14.
- David’s son, Solomon, was the person to build the temple, 2 Sam 7:12, 13.
- David and his descendants must remain faithful to God and keep all that is written in the Book of the Law (Deuteronomy), Deut 17:18, 31:26.
Note that the Davidic Covenant was distinct from the Israelite and Levitical Covenants – David became a type of the eternal reign of Messiah to come.
While David and his successors were earthly kings, they were to recognise that the real king of Israel was God. 1 Sam 8:7, 8, 24:6, 2 Sam 19:21, 1 Chron 28:5, 2 Chron 9:8, 13:8, Ps 5:2, 44:4. See also 1 Sam 12:14.
It is a simple matter of history that David’s (earthly) descendants were not always faithful and the earthly Davidic dynasty ended in 586 BC with the final capture of Jerusalem by Nebuchadnezzar. However, the New Testament calls Jesus Christ, Messiah, “the Son of David” as a direct fulfilment of the (ultimately) eternal throne of David which Jesus inherited. Matt 1:1, 20, 9:27, 12:23, 15:22, 20:30, 15, 21:9, 15, Mark 10:35, Luke 1:32, 33, 18:38, 39, John 1:49, Acts 13:32-37, Heb 1:8. See also Rev 11:15, 19:16. Such a Messiah was prophesied long ago: Ex 15:18, Ps 10:16, 61:7, 68:16, 92:8, 93:5, 146:10, Isa 9:7, 47:7, Lam 5:19, Micah 4:7, etc.
Note especially, what the angel said to Mary before Jesus’ birth in Luke 1:32, 33 –
He will be great and will be called the Son of the Most High. The Lord God will give Him the throne of His father David, and He will reign over the house of Jacob forever. His kingdom will never end!”