Is David a Priest?

David is from the tribe of judah, and we also know that you can only be a priest if you are from the family of levi. And so when david puts on an ephod, he's wearing the clothes of a priest. He even seems to participate, in a certain way, in the actions of the priest. David not only foreshadows jesus's being a king, but also foreshadows, in some ways, a priesthod of melchisedek.