Well, I admit I didn't listen to the whole teaching. When he said "no old, no new covenant, there's only one" my immediate reaction is that he is deviating from what the scripture states, according to my understanding of it. If he is redefining covenant by a different usage of the term than how scripture is using it, all bets are off. To answer your question, the earlier priesthood is a higher authority than the Aaronic, just as Abraham's tithe was a higher authority than the Levitical. I take it the point of this in Hebrews is that Jesus' priesthood is a higher authority than the Levitical. And the distinction the writer of Hebrews makes is that the New Covenant is a higher authority and more permanent than the old, it being a spiritual covenant rather than a material one. So then it begs the question why does Alan say there is not a New Covenant? To be honest, I'm not willing to sit through 47 minutes of getting his perspective to try and figure that out.
TD