In Forgotten History
, there's a Betelgeusian (a male, I believe*) serving on the Federation Council. However, it didn't say whether he represents the Betelgeusians (or some division of them) or whether he's simply a citizen of one of the established Federation worlds. Given the decentralized and nomadic nature of the Betelgeusians, I was reluctant to come to any conclusions.
* Males are more likely to be away from the Prides than females, since all of them spend their adolescence as wanderers anyway; some presumably don't go back?
I almost promoted Algol to the "established" list, given that every appearance by an Algolian, both on screen and in the novels, has involved their participation in Federation matters, but I'm waiting for something more on that one.