I think what would be awesome is if, that somehow there are Precursors that are still alive. Continuing from Halo 5's story, the Warden and the other Guardians lose faith in Cortana and decide to serve the Precursors instead. The Guardians deem their leaders as more fit to rule.
Different life forms from what we have already seen in Halo are also recruited (We do not yet know why the Precursors are recruiting, just that they are).
While this is going on a new Prophet emerges and attempts to revive the covenant or what is left of it. This Prophet struggles as their is bad blood between the Elites and the Brutes. But somehow differences are settled and he Covenant is back once again.
The civil war on Sangheilios effectively comes to an end.
The have been few flood contacts in recent time and this has become a bit of a concern to the UNSC. The are also unerring rumours that Didact may still be alive, knowing he fell into some sort of slip space portal, this unsettles some higher ups within the UNSC.
A lot going on I know
Not sure exactly how exactly all this would be able to put into one game, but it would be damn cool if 343 did somehow.
We find out in the game exactly what is going on with all our new enemies and mysteries.
It is then up Master Chief to team up with Cortana, the Arbitar, Blue Team, Fireteam Osiris, and Dr Halsey to combat these threats. Heroes will rise once again.