To be sure, as with many things eschatological in the New Testament, we don't get a very detailed and wholly consistent vision of Judgment Day across all the NT writings, but we do find things like Matthew 25:
“When the Son of Man comes in his glory, and all the angels with him, he will sit on his glorious throne. All the nations will be gathered before him, and he will separate the people one from another as a shepherd separates the sheep from the goats. He will put the sheep on his right and the goats on his left."
And Revelation 20:
Then I saw a great white throne and him who was seated on it. The earth and the heavens fled from his presence, and there was no place for them. And I saw the dead, great and small, standing before the throne, and books were opened. Another book was opened, which is the book of life. The dead were judged according to what they had done as recorded in the books. The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and each person was judged according to what they had done.
Obviously, we see a development from the Old Testament "the Day of the Lord," which is mainly a vision of Israel's vindication within history among the nations, to something much more universal and cosmic, a time where each person will be "judged according to what we have done."
As has been the theme of this series, this contrast between the Old and New Testaments can seem discontinuous, but if we pay attention to intertestamental writings, like 1 Enoch, we find a more continuous development. Judgment Day is another example of this.
For example, from 1 Enoch 69:
And he sat on the throne of his glory,
and the whole Judgment was given to the Son of Man,
and he will make sinners vanish and perish from the face of the earth.
And from 1 Enoch 100:
And the Most High will be aroused on that day
to execute great judgment on all.
He will set a guard of the holy angels over all the righteous and holy:
and they will be kept as the apple of the eye
until evil and sin come to an end.
All that to note that the notion of Judgment Day isn't a novelty introduced by the New Testament but a development that occurred within Second Temple Judaism, a development that informed the vision of Judgment Day we find in the New Testament.