What was the Star League's ultimate endgame? I don't know that they had one besides maintaining their power and dominance.
Say, for a moment, that I were ilKhan of ilClan Wolf, having just absorbed the battered remains of the Republic. Personally, my approach would be to start forming a Star League not out of raw conquest, but out of a mix of warfare and diplomacy and diplomacy induced warfare, maybe even some warfare induced diplomacy. After rebuffing the inevitable refusal by the Jade Falcons and seeing Malvina dead, hopefully we would be looking at a wounded Clan Jade Falcon with more to gain by allying with Clan Wolf than opposing it. The Sea Foxes are in a position to profit from participating in our new Star League and are already something of an ally. Three out of Six is a pretty strong position in the joke that is the Council of Six, to whatever extent that still even persists.
Personally I would not expect terribly much out of the Bears, Horses and Ravens other than an acnowledgement that I have in fact fulfilled the conquest of Terra and am as such, due the bragging rights of being the ilClan. They are welcomed to participate in our revival of the Star League, but I want them as allies and willing participants, not sullen vassals. I suspect that should we leave the Bears and Ravens to conduct their business as usual, that they would count themselves in, and the Horses seem like they would not want to exclude themselves from a Third League either.
I would consolidate power in what was Prefecture X, forming something of a Wolf Hegemony, and shrink the borders of the Wolf Empire in the FWL somewhat. I would move some of the manufacturing we established there, to Terra and this Hegemony for better defensibility, and use some of those lost worlds as an enticement package to get the Free Worlds League and Lyrans to sign on with our League. Likewise, with the Combine and Confederation bearing down on the Federated Suns, I would offer them a chance at survival through Membership in our League.
I would direct the Bears and Ravens to pursue gains against the Draconis Combine, for several reasons. First, to make good on the promise to take pressure off of the Federated Suns, but also because in the fall of the original star league, the Combine was one of the petty parties who refused to acknowledge the rightful succession following the fall of the Camerons. For this, we have a score to settle. With the Combine, I would be willing to hear a plea for peace, a pledge to join our Star League, after our pound of flesh has been taken, and our Bears and Ravens sated on dragon meat.
Likewise, the Confederation is an enemy of the Republic, whose surviving members are now a part of our clan. And they too denied the succession orders. And they covet worlds we now control. Unlike the Combine, I am disinclined to accept their surrender. An example needs to be made, a demonstration of the might of our new Star League. On the off chance that the Capellans are willing to play by Clan Rules, and fight honorably, I wil settle for driving them back to their Pre-blackout borders. If they play dirty, however, I will indulge in excess and make the Fourth Succession War look like a fraternity prank.
Once I have the other Clans on board with my League, and have dealt, one way or another, with the Successor States, I would focus on consolidation and innovation. Work on promoting aspects of Clan Culture throughout our League, primarily the practice of conducting warfare through Trials, and encouraging the startup of Warrior breeding programs so that Civilians do not have to suffer the hardship of the life of a Warrior. I would work on boosting the technology levels of everyone in the league, with both the Star League and the Golden Century as inspirations.
Post-consolidation, the Golden Century really would be my template for how things would be, minus the scaricity issues of the Homeworlds. I would rebuild a multinational, multiclan, Star League Defense Force as an enforcement arm and force to defend the league from those without. Be they Periphery faction or holdouts who refused to join the league.
Within the Clans of my League, I would set forth another goal. A Competitive goal, for the five non-wolf Clans of the Star League. Long Ago, our wayward kin in the homeworlds rejected us and drove us from the homeworlds in the wars of reaving. Rather than forever wonder whether they shall be returning, rather than let them remain some great unknown, we shall return to the Clan Homeworlds. Much as in Operation REVIVAL we shall sortie forth, to reclaim what is rightfully ours. The Clan or Clans who retake Strana Mechty will be venerated within our League, and honored as a peer of the ilClan. But there is no style in reclaiming Strana Mechty first, no First, reclaim your ancestral worlds, and demonstrate the strength of our League to whatever has become of the Clans of the Homeworlds.
Clan Wolf will see to the Inner Sphere, and provide a support force to this expedition, but it will be on the other five clans to do the Retaking. As a Wolf, however, I WOULD remember our ancient bonds to the Coyotes, and offer them a chance to join the League rather than be consumed by it. Offer them Safcon to the Inner Sphere, and a chance to build anew with us. The Escorpion Imperio would not be an explicit target of this expedition, but neither would it be a forbidden target.
Beyond that, I would direct parts of the League to investigate the triple boogeymen of the Word of Blake, any not-eradicated vestiges of the Society and the Not-Named, seeking out the ultimate fate of those factions, ensuring their elimination.
Exploration of the Deep Periphery would be another goal.
If their genetic materials were recovered, I could see birthing new sibkos from Extinct Clans, bringing those clans back to life as provisional members of our new Star League, giving them a chance to bear witness to our glory, and a chance to rebuild themselves. Fallen or not, their roots lead back to the Star League. If they are truly unworthy, then they will not survive. If there is yet value there, they might thrive. Excepting, of course, the Not-Named and technically, the Absorbed clans would be part of the clans that assimilated them.
Canon events may lead another direction, but I think, as laid out above, there is much for an ilClan to busy itsself doing. Everything I laid out above could easily outlast a single ilKhan's lifespan, if not two or three.