NO; The David covenant is for a King from him to rule forever (Jesus):-

Psalm 89:34-36 NWT "I will not violate my covenant Or change what my lips have spoken. 35 I have sworn in my holiness, once and for all; I will not tell lies to David. 36 His offspring will endure forever; His throne will endure like the sun before me."

The New Covenant is between God; Jesus; and Jesus diciples who go, in the future, into the Heavenly Kingdom and rule with Jesus (see 2 Tim. 2:12):-

The New Covenant:-

Luke 22:20 NWT "“This cup means the new covenant by virtue of my blood, which is to be poured out in your (the 11 firstly) behalf."

&

Luke 22:28-29 NWT “However, you are the ones (the 11, Judas has left) who have stuck with me in my trials; 29 and I make a covenant with YOU (the 11), just as my Father has made a covenant with me, for a kingdom,"

NO; The Davidic covenant is for a King from him to rule forever (Jesus):-

Psalm 89:34-36 NWT "I will not violate my covenant Or change what my lips have spoken. 35 I have sworn in my holiness, once and for all; I will not tell lies to David. 36 His offspring will endure forever; His throne will endure like the sun before me."

The New Covenant is between God; Jesus; and Jesus diciples who go, in the future, into the Heavenly Kingdom and rule with Jesus (see 2 Tim. 2:12):-

The New Covenant:-

Luke 22:20 NWT "“This cup means the new covenant by virtue of my blood, which is to be poured out in your (the 11 firstly) behalf."

&

Luke 22:28-29 NWT “However, you are the ones (the 11, Judas has left) who have stuck with me in my trials; 29 and I make a covenant with YOU (the 11), just as my Father has made a covenant with me, for a kingdom,"