Given that Alaric Wolf/War/Steiner(-Davion) is almost certainly named for Alaric I, king of Visigoths, who sacked Rome, i'd say the Republic of the Sphere is the Western Roman Empire. It doesn't help it uses Roman terminology for its various organizations and organs, and the abbreviation for it, ROTS brings mind SPQR...
And yeah, i figure Alaric becomes the IlKhan and the Wolves the IlClan.
More likely, the Third League is kind of a Holy Roman Empire (which was neither Holy, Roman nor an Empire). It won't be a real Star League, it won't uphold the legacy of the Terran Hegemony and it won't be an alliance for it is almost certainly forged in fire and held together by fire...
EDIT That said, the Third League probably has shades of the Eastern Roman Empire. Indeed, the Star League as a whole is something of a Rome for the BT-verse, the legacy will be brought up again and again for variety of reasons.
EDIT2 Late realization that you talked about the Republic of the Sphere and i jumped to Star League from that. This is because i tend to see ROTS as a Star League's successor state in a sense.