Ok, so I'm playing as the Byzantines and through a untimely death and then assassination that I had absolutely nothing to do with I inherited the Kingdom of Georgia...my question is what I should do with this. I still have Gavelkind succession, so I don't want to risk splitting my kingdom on monarch death. My question is, can I grant the kingdom to a vassal without losing them as a vassal...or will they become independent if I do grant them the kingdom. It seems like they would still be my vassal since the Empire rank is above the king rank, but I just wanted to ask and make sure. Will also keep some of my nobles from griping about wanting the kingdom even though they don't have a claim to it
No, just empires. I would try to make Georgia a primogeniture succession law first (you'll have to wait ten years). Giving it to your primary heir is a good idea, though you may want to make it a priority to keep a land connection between Georgia and Byzantium.
If you are say King of France and you inherit England, giving England to your heir will make him independent though your ally in any wars that come along. Sometimes it is best to have a bunch of allied realms than one huge empire. Less plotting, and wars get easier to run.