It would have to go back to its role of actually helping people, and being advisers. Literal advisers, not meddling manipulators. They have be the Cold White Stark Tower. They need to become the warm, compassionate and helpful tower (I don't mean push over weak tower, though, just to be clear)

The Greens and Reds would need to change themselves for obvious reasons. No Last Battle and no insane male channelers. However with the Seanchan problem, the Greens could just shift their focus there, and the Reds could maybe EVENTUALLY become the go between of the WT and the BT.

The Blues might fall kind of funny if the WT holds to not becoming political manipulators any more. I don't think their purpose would change, but their methods would likely have to.

And, of course, Integration with other channeling groups will be integral to their survival.