“Being therefore a prophet, and knowing that God had sworn with an oath to him that he would set one of his descendants on his throne, he foresaw and spoke about the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption. This Jesus God raised up, and of that we all are witnesses. Being therefore exalted at the right hand of God, and having received from the Father the promise of the Holy Spirit, he has poured out this that you yourselves are seeing and hearing. For David did not ascend into the heavens, but he himself says,‘The Lord said to my Lord, “Sit at my right hand, until I make your enemies your footstool.”’” (Acts 2:30-35)
It’s hard for me to believe that Dispensationalists would claim that Jesus is not the Davidic King reigning right now on the Davidic throne over the eternal Kingdom of God promised to David’s Son. That view has however become a minority as classical and revised dispensationalists are either on or nearing the theological endangered-species list (at least in academic and biblical-theology circles). Among the numerous responses that I’ve found helpful, here are some quotes from Progressive Dispensationalism (which on a spectrum is closer to Covenant Theology than Dispensational Theology) by Craig Blaising and Darrell Bock.
Craig Blaising and Darrell Bock bring up three of the most common classical or revised dispensational objections to Jesus’ reign as Davidic King. I’ll mention the first two and quickly summarize their response (although I recommend reading this section in their book in its entirety).
In sum: “Beginning in Acts 2, Jesus’ apostles began to preach that His resurrection was the fulfillment of the covenant promise to ‘raise up’ David’s descendant. The promise to raise up a descendant, in 2 Samuel 7:12, is connected with the promise to establish His kingdom or, putting it another way, to establish His throne. Peter argues in Acts 2:22-36 that David predicted in Psalm 16 that this descendant would be raised up from the dead, incorruptible, and in this way, He would be seated upon His throne (Acts 2:30-31). He then argues that this enthronement has taken place upon the entrance of Jesus into heaven, in keeping with the language of Psalm 110:1 that describes the seating of David’s son at God’s right hand.” (p. 177)
Objection 1. “The throne Jesus received at His ascension was not the throne promised to David.”.
“First of all, the objection fails to observe the fact that every New Testament description of the present throne of Jesus is drawn from Davidic covenant promises….In Acts 2:30-36, the resurrection, ascension, and seating of Christ in heaven at the right hand of God (Ps. 110:1) are presented in light of the prediction ‘that God had sworn to him [David] with an oath to seat one of his descendants upon his throne’ (Acts 2:30). No other throne is discussed in this text except the Davidic throne.” (p. 182)
“The second problem with the objection is that it fails to comprehend the relationship between God’s heavenly rule over Israel and the rule of His chosen king….Because of the covenant orientation of the heavenly throne to Israel, Jesus’ enthronement there makes Him the Christ, the anointed king of Israel. And because God, the King of Israel, had covenanted to David that his descendant would rule Israel and all the nations, this installation of Jesus (the son of David whom God has raised up from the dead) in heaven by the divine King of Israel portends an imminent descent to the Jerusalem throne.” (pp. 184-85)
Objection 2. “Jesus’ present activity is best understood as divine sovereignty, not Davidic kingship.”
“First of all, we note that the Bible explains Jesus’ present activity in Davidic as well as divine terms….Repeatedly through the Book of Acts and the Epistles, it is as the Christ (that is Messiah, the anointed Davidic king of Israel), seated at the right hand of God (the Davidic position) that He is active today.” (p. 185)
Craig A. Blaising and Darrell L. Bock, Progressive Dispensationalism (Grand Rapids: Baker, 1993), 174-283. Pages 182-187 are worth reading in their entirety.