There is no 'priesthood' in the church of God, let alone a valid one...
Priest are valid only, 'under the Law'...And Christians are not under the Law...
The Mosaic priesthood is valid only under the Law. But I don't think we can say that about the concept of priesthood in general
Peppered all over Hebrews is that Christ is a priest "according to the order of Melchisedek." So there's at least one priesthood that's ongoing.
And when you start thinking about a) what it means to be of the "order of Melchisedek", and put that together with His solemn command to b) "do this in memory of me", I think it all makes more sense.