The word Tabernacle denotes a dwelling place, often a tent.
AV Hebrews 11:9 By faith he (Abraham) sojourned in the land of promise, as in a strange country, dwelling in tabernacles with Isaac and Jacob, the heirs with him of the same promise:
Moses had his own tabernacle (or tent) that he lived in but he was instructed to build a tabernacle where God could dwell with Israel. I make the assumption that this is what you are referring to as the Tabernacle of Moses.
Exodus 25:8 "And let them make Me a sanctuary, that I may dwell among them. 9 "According to all that I show you, that is, the pattern of the tabernacle and the pattern of all its furnishings, just so you shall make it.
The details of its construction are given in Exodus 26. Stephen refers to it.
Acts 7:44 "Our fathers had the tabernacle of witness in the wilderness, as He appointed, instructing Moses to make it according to the pattern that he had seen,
James speaks of the Tabernacle of David.
Acts 15: "Simon has declared how God at the first visited the Gentiles to take out of them a people for His name. 15 "And with this the words of the prophets agree, just as it is written: 16 ‘After this I will return And will rebuild the tabernacle of David, which has fallen down; I will rebuild its ruins, And I will set it up; 17 So that the rest of mankind may seek the LORD, Even all the Gentiles who are called by My name, Says the LORD who does all these things.’
He is quoting from a prophecy of Amos (from the Septuagint translation).
Amos 9:9 For I will give commandment, and sift the house of Israel among all the Gentiles, as corn is sifted in a sieve, and yet a fragment shall not in any wise fall upon the earth... 11 In that day I will raise up the tabernacle of David that is fallen, and will rebuild the ruins of it, and will set up the parts thereof that have been broken down, and will build it up as in the ancient days: 12 that the remnant of men, and all the Gentiles upon whom my name is called, may earnestly seek me, saith the Lord who does all these things.
We can see from the context that the Jews were to be scattered and ‘sifted’ among the nations and the Tabernacle (meaning the house and kingdom) of David would be restored not just for Israel but also for the gentiles who would earnestly seek him.
This is referring to the restoration of David’s kingdom at the return of Christ.
Isaiah 9:6 For unto us a Child is born, Unto us a Son is given; And the government will be upon His shoulder. And His name will be called Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace. 7 Of the increase of His government and peace There will be no end, Upon the throne of David and over His kingdom, To order it and establish it with judgment and justice From that time forward, even forever. The zeal of the LORD of hosts will perform this.
Isaiah 16:5 In mercy the throne will be established; And One will sit on it in truth, in the tabernacle of David, Judging and seeking justice and hastening righteousness."
Luke 1:31 "And behold, you will conceive in your womb and bring forth a Son, and shall call His name JESUS. 32 "He will be great, and will be called the Son of the Highest; and the Lord God will give Him the throne of His father David. 33 "And He will reign over the house of Jacob forever, and of His kingdom there will be no end."
In conclusion the Tabernacle of Moses was replaced by the Temple of Solomon and both are no more. The Tabernacle of David is the City, throne and kingdom of David which will be rebuilt and restored when Christ returns to rule this earth in righteousness.
I hope this helps.