4. Prediction of the New Covenant That Would Come: Another passage in the context of Jeremiah 30:24 is Jeremiah 31:31-34 -- a prophecy that predicts that the New Covenant would come at the end of the Old Covenant.  The writer of the book of Hebrews  verifies this in Hebrews Chapter 8. The New Covenant for His people prophesied in Jeremiah 31 is fulfilled in the First Century, and the Old Covenant is becoming obsolete in Hebrews 8:13. Again, we see the last days of the Old Covenant were upon them in the First Century. The whole context of Hebrews 8 is again stated in the context of Hebrews 1:1-2. 

5. Jesus Was Born in the 'Last Days'Micah 4 shows that Jesus was born in the last days of the Old Covenant: "And it will come about in the last days,  that the mountain of the house of the LORD will be established as the chief of the mountains. It will be raised above the hills, And the peoples will stream to it." In the same context, Micah 5:2 reads: "But as for you, Bethlehem Ephrathah, too little to be among the clans of Judah, from you One will go forth for Me to be ruler in Israel. His goings forth are from long ago, from the days of eternity.”

This prophecy is fulfilled in the last days of the Old Covenant according to Matthew 2:1-6:

"Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, magi from the east arrived in Jerusalem, saying,  “Where is He who has been born King of the Jews? For we saw His star in the east and have come to worship Him.”  When Herod the king heard this, he was troubled, and all Jerusalem with him. 4 Gathering together all the chief priests and scribes of the people, he inquired of them where the Messiah was to be born.5 They said to him, “In Bethlehem of Judea; for this is what has been written by the prophet:

‘AND YOU, BETHLEHEM, LAND OF JUDAH,
ARE BY NO MEANS LEAST AMONG THE LEADERS OF JUDAH;
FOR OUT OF YOU SHALL COME FORTH A RULER
WHO WILL SHEPHERD MY PEOPLE ISRAEL.’”

(Cross references: Deuteronomy 31:29Judges 2:19)

6. Isaiah's Prediction of judgment on Old Covenant Israel in the Last Days: In Jeremiah 30:24: Jer 4:8, Jeremiah 30:24: Jer 23:20

 Isaiah 2:1-2 , we see almost verbatim the words from Micah 4:1,  about the last days of the covenant:

"The word which Isaiah the son of Amoz saw concerning Judah and Jerusalem.

Now it will come about that

In the last days 
The mountain of the house of the LORD
Will be established as the chief of the mountains,
And will be raised above the hills;
And all the nations will stream to it

This segment of Scripture is full of description of the last days that can be traced through the New Testament to the book of Revelation. In the same context of Isaiah 2 is the parable of the vineyard (Isaiah 5:1-7) – the Vineyard is the house of Israel! (vs 7). It is a vineyard that God said produced worthless grapes! This same parable Jesus quotes in Matthew 21:33-46.  Verses 40-45 Jesus describes what is coming upon the Jews in their last days.  The Pharisees, being familiar with the prophet Isaiah's words,  knew exactly what Jesus was saying, and that Jesus spoke the parable about them. The end of the Old Covenant system ended at the Cross, yet the final destruction of the temple system came in 70 A.D.