They will rule one after the other. This can be stated explicitly. Alternate translation: "ten kings will rule over this fourth kingdom, one after another" (See: [[rc://en/ta/man/translate/figs-explicit]])
This other king is not one of the ten. It may be helpful to refer to him as "the eleventh king." Alternate translation: "after that an eleventh king will become powerful" (See: [[rc://en/ta/man/translate/figs-explicit]])
He will defeat three of the original ten kings. It may be helpful to state that those three kings are represented by the three horns that were pulled out. Alternate translation: "he will defeat the three kings that were represented by the three horns that were pulled out" (See: [[rc://en/ta/man/translate/figs-explicit]])