When will the 10 kingdoms of Revelation arise?

The 10 world leaders arise during the final Gentile kingdom and before the antichrist appears, who will subdue three of these kings after he gains power:

Dan. 7:23  “Thus he said: ‘The fourth beast will be a fourth kingdom on the earth, which will be different from all the other kingdoms and will devour the whole earth and tread it down and crush it.
Dan. 7:24 ‘As for the ten horns, out of this kingdom ten kings will arise; and another will arise after them, and he will be different from the previous ones and will subdue three kings.

The book of Revelation says the antichrist (the “beast”) gains his power at the midpoint of Tribulation after dying and being resurrected by Satan:

Rev. 13:1 And the dragon stood on the sand of the seashore. Then I saw a beast coming up out of the sea, having ten horns and seven heads, and on his horns were ten diadems, and on his heads were blasphemous names.
Rev. 13:2 And the beast which I saw was like a leopard, and his feet were like those of a bear, and his mouth like the mouth of a lion. And the dragon gave him his power and his throne and great authority.
Rev. 13:3 I saw one of his heads as if it had been slain, and his fatal wound was healed. And the whole earth was amazed and followed after the beast;
Rev. 13:4 they worshiped the dragon because he gave his authority to the beast; and they worshiped the beast, saying, “Who is like the beast, and who is able to wage war with him?”

Later in Revelation we read:

Rev. 17:12 “The ten horns which you saw are ten kings who have not yet received a kingdom, but they receive authority as kings with the beast for one hour.
Rev. 17:13 “These have one purpose, and they give their power and authority to the beast.

Rev. 17:17 “For God has put it in their hearts to execute His purpose by having a common purpose, and by giving their kingdom to the beast, until the words of God will be fulfilled.

So the rise of the ten kings precedes the arrival of the antichrist at the start of Tribulation. However, during the midpoint of Tribulation, the death and resurrection of the antichrist leads to the killing of three of these kings. From that time, the world will be ruled by the antichrist alone, with the seven remaining kings giving their power to the antichrist. 

The church will not be present on earth for these events. We are removed from the earth prior to the start of Tribulation. Though the church may be on earth for the arrival of the ten kings, we will not see the arrival of the antichrist or the start of the Tribulation. 

Scripture quotations taken from the (NASB®) New American Standard Bible®, Copyright © 1995, 2020 by The Lockman Foundation. Used by permission. All rights reserved. www.lockman.org