I think the Bible explains what Christs Kingdom is, but I think He already rules, there isn't some 'changing of rulership' going on.. in fact I find that concept sort of strange, like handing over a crown or something, I don't think that the earthly rulership means that Jesus is 'waiting' for kingship.
Also, to add, the NT was written by man, yes, inspired, but man authorship is also prone to conforming to pre-existing ideas of how the Divine nature of Jesus is portrayed and other concerns. I think we need to read between the lines sometimes, for example the Deityship of Jesus, it doesn't 'happen' at a certain point, it already is established. We are going to disagree on this, I already know, because of our denominations.