Isaiah 66:19-21

It spoke of God appointing people to service as Levitical priests. He doesn't do that anymore. It's never happened since the first century AD. It was therefore fulfilled in Old Covenant times. 

Also the nations named don't exist anymore.

And if they do, they certainly won't use archery as weaponry!

Nor mules and chariots as means of international travel.

All those details date the fulfilment of the prophecy.

It didn't mean Gentiles would be appointed priests and Levites. They weren't then - and there never will be a time. It never said He would.

It said He would make some of the Jews and their children priests and Levites, as follows:

God's reputation would increase in the nations to such an extent that Gentiles would become motivated to transport Jews and their children back to the land of Israel, in an act of their devotion - their offering, so to speak - to God, just as Israel itself used to offer their offerings to God; and just as Israel's offerings had once been clean, so God would once again view His people the Jews and their children favourably in their land; and some of them (some of those repatriated Jews and their children) would then once again begin functioning as priests and Levites. It never meant Gentiles would!

At the return from captivity, even some of the priests were rejected from the priesthood if they couldn't prove their descent by genealogy from Levi. 

So "some of them" meant that they had to be not only Jews, but that also had to be descended from Levi - and be able to prove it. That's why it said, "...some..."

There has been the fulfilment of all those precise details.

If there had not been, then there would have been no Temple, no Levites and no Jerusalem for Messiah to later suddenly come to and again purify (Malachi 3:1-6).