Probably Filoni, which I know is probably a not-so-popular take on this sub for some reason, but he's the closest thing to a successor to Lucas as there is. The handoff should've been gradual though, ideally Lucas would've been around to oversee the sequels, and after that Filoni would be overseeing the canon.

Though some here aren't fans of the Filoni interpretation of SW, what we get from Filoni are a few things that aren't found in many others, primarily someone who understands George Lucas and (by extension) the philosophy of Star Wars, and someone who has enough understanding of it to oversee the canon themselves in the future.

Though Filoni may not have the acumen to be the main head of the company, ideally he would be a head of story in some capacity. As of a few years ago, I believe he was actually promoted to some kind of position as head of story.

Though Filoni probably wasn't ready for this in 2012. Lucas should've remained involved...and Kathleen shouldve done more to protect Lucas's company and his vision. And Iger should've honored the agreement to follow Lucas's stories. And Abrams should've kept more to Lucas's sequels.

Alternatively, Star Wars should never have been sold off in the first place. The "should've's" never end.