This is going to be a pretty spoileriffic discussion of Legion stuff, though it's going to be mostly speculation. I'll start with a bit of spoiler-free background.
Genn Greymane is oddly both one of the Alliance's oldest and newest leaders. Way back in the era of the Second War, Anduin Lothar - fleeing from a Horde-occupied Stormwind - was working to rally the other human nations to the cause of defeating the Horde. He found his most reliable ally in the altogether good guy, King Terenas of Lordaeron. Terenas championed Lothar's cause, pledging his kingdom - the largest human kingdom other than the devastated Stormwind - to provide a nice strong base of force upon which to build the Alliance. The other kingdoms - Kul Tiras, Dalaran, Alterac, Stromgarde, would join relatively eagerly (though Alterac would sell out the Alliance once things turned difficult to save their own skins - which is why you don't see a lot of Perenolde kings running around these days.) However, for Gilneas, this was a bit of a conundrum.
The very character of Gilneas was one of independence. They industrialized far sooner than the rest of the human kingdoms, achieving something of an 18th or even 19th century technological level while the rest were still limited to swords and arrows (not that they haven't made those work in Warcraft's lovely schizo tech setting.) Gilneas was relatively isolated on a peninsula. They weren't quite the naval superpower that Kul Tiras was, but they had a strong navy. Genn, whose father Archibald had instilled in him self-reliance as a core value, was extremely skeptical of this "Alliance" Lothar and Menethil were proposing. He felt that he could defend his lands against this "Horde" threat, and that it wasn't his concern if they were attacking other people.
Still, they managed to get him to commit at least a token force. But once the war was finished, Terenas advocated putting the Orcs in internment camps rather than just slaughtering them en masse. (Of course, the camps were really the lesser of two evils, and one that the Orcs uses as its only real rallying cry to make themselves seem the victims of the Alliance.) Genn had no interest in allowing the beasts to live - especially if the constituent nations of the Alliance were all going to have to shoulder the cost of maintaining these camps and providing land for them. So Genn had a new solution that (he thought) would be a nice permanent solution to all of the Orc/Alliance problems. He built the Greymane Wall, intending to simply let the rest of the world deal with its own problems while he worried about his own.
Isolated for decades, Gilneas had three major problems to deal with. First, there was the Northgate Rebellion - a direct reaction to Darius Crowley's loss of essentially all of his land now that it was cut off by the wall. Second, the Worgen began to rampage through the country (secretly a Forsaken plot, actually.) Finally, when the Cataclysm shattered the Greymane Wall, the Forsaken invaded, which ended with the evacuation of most of the Gilneans from their country (many of whom had been turned into Worgen by then, including Genn himself.)
Out of necessity, as well as a respect for the Night Elves who understood the nature of their curse and aided them in controlling it, Gilneas re-joined the Alliance.
We haven't actually seen much of them since, outside of the occasional NPC. But thing will be changing in Legion.
It appears that not only is Varian Wrynn going to die in the opening battle against the Legion, but Vol'jin will either do the same or at least wind up incapacitated or missing, leaving Sylvanas Windrunner as the new Warchief (or at least "Acting Warchief," though to be fair, that was Garrosh's official title when Thrall went off to deal with the Cataclysm.)
While Sylvanas has made plenty of enemies over the years as the Banshee Queen, probably no single person hates her more than Genn Greymane. She invaded his country and sent his people into exile (I don't even know if he knows about her collaboration with Ralaar Fangfire to infect his people with the Worgen Curse,) and on top of all that, she killed his beloved son, Liam.
And while Genn is a man in his 70s, I'd assume that the Worgen Curse has reinvigorated him, making him a deadly feral beast on the battlefield. If there's any issue around which a new conflict between the Alliance and Horde would ignite, it's the ongoing struggle for Gilneas.
Sylvanas becoming Warchief would be a hugely provocative move for the Horde, but the much bigger danger is what happens in the Alliance.
Varian was already a generation younger than Genn, and now Anduin - who is now an adult, certainly, and even has some experience as "Acting King" while Varian was missing - will be the King of Stormwind, young enough to be Genn's grandson.
Not counting his absence after the Second War, Genn Greymane is actually the senior faction leader within the Alliance. The Dwarves and Gnomes would join later, and the Night Elves wouldn't join until after the Third War. People didn't even realize the Draenei existed at that point.
While I think the assumption is that the High King of the Alliance is going to be a position passed down from Wrynn to Wrynn as long as they can, along with the title of King of Stormwind, we don't know that that's how it's organized.
Genn has lived most of his life with absolutely no person to answer to. The Alliance has been a necessity, due to the curse and his exile. But I wonder if Genn will see Varian's death as an opportunity. Surely they couldn't let a child like Anduin lead the might of the Alliance? And as ancient and wise as Tyrande and Velen might be, they do not have the legacy to lead the human lands. Now would be the opportunity for Genn to take the reins of the Alliance. For too long, they have tolerated this stalemate in Gilneas. They ended the war against Garrosh without resolving the issue of Lordaeron.
In this time of great strife, the Alliance needs a strong leader with experience, but also the will to fight. Perhaps it is time that Genn Greymane becomes High King, and shows the rest of the Alliance the effectiveness of the Gilnean way.
And first things first, we kill Sylvanas.