I think it’s the adverb πρότερον which modifies τῶν μέντοι βασιλέων with a repetition of the article.
The construction is article noun article modifier (adj./adv./pron./prep. phrase/etc.).
I have just reread what Taylor says on sandwich forms. The inner part of the sandwich (ie πρότερον in this case) specifies which of of the outer part is being talked about. He was a little laconic but with your pointer it all makes sense.
(I’m not sure what gave me the idea there must be grammatical agreement between the inner and outer part.)
Smyth explains both of the idiomatic usages here in secs. 1096 and 1158. Sec. 1096: πρότερον is an adverb used as an adjective. Sec. 1158: Instead of των [μεντοι] πρότερον βασιλεων, “of the previous kings”, art. - attributive adverb - noun, he writes των μεντοι βασιλεων των προτερον, art. - noun - art. - attributive adverb. This isn’t as common as putting the attributive word between the article and the noun, but it’s quite common in Greek.