It came up after the ten horns | Justinian decrees

After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns. I considered the horns, and, behold, there came up among them another little horn (Daniel 7:7-8).

The Roman Catholic Church grew in power after Constantine accepted Christianity, but it did not control secular affairs until the Justinian decrees went into effect. The power of the bishop of Rome steadily increased and papal authority in secular affairs arose after the Barbarian division of Rome in 476 AD.

The American Catholic Quarterly Review says this:

Long ages ago, when Rome through the neglect of the Western emperors was left to the mercy of the barbarous hordes, the Romans turned to one figure for aid and protection, and asked him to rule them...and thus...commenced the temporal sovereignty of the popes. So, meekly stepping to the throne of Caesar, the vicar of Christ took up the sceptre to which the emperors and kings of Europe were to bow in reverence through so many ages.ⁱ

William Barry says this:

The Pax Romana has ceased; it is a universal confusion. But wherever a Bishop holds his court, religion protects all that is left of the ancient order. A new Rome ascends slowly above the horizon…the heir of religion which it has overthrown; it assumes the outward splendour of the Caesars…The emperor is no more...But the Pontifex Maximus abides; he is now the Vicar of Christ, offering the old civilisation to the tribes of the North. He converts them to his creed, and they serve him as their Father and Judge Supreme. This is the Papal Monarchy, which in its power and its decline overshadows the history of Europe for a thousand years.ⁱⁱ

The rise of the little horn occurred after the subdivision of Rome into ten powers in 476 AD. At this time, the little horn became firmly established in order to qualify as a horn, that is, to be a king or a kingdom:

And the ten horns out of this kingdom are ten kings that shall arise: and another shall rise after them (Daniel 7:24).

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i. American Catholic Quarterly Review (April 1911).

ii. William Barry, The Papal Monarchy: 45-46.