Of course it's not Garth. It's Lazarus.
I don't think we'll see Khan in this movie but I think he'll be in the background indirectly. He'll likely figure more prominently in the next movie, though I can imagine scenarios where he is not central to the story (perhaps as a flashback--Abrams loves them--that ties into events set up in this movie). Or maybe he'll be the main adversary in the next film. But nothing I've seen or read about the current film makes me think Khan will be a major character this time out.