PRIESTLY VESTMENTS are being reconstructed (as far as that is possible, given our limited knowledge) by the Temple Institute:

Third Temple preparations begin with priestly garb
By DANIELLE KUBES

Wearing a turban and a light blue tunic threaded with silver, a man stands in a workshop in Jerusalem's Old City beside spools of white thread affixed to sewing machines. A painting of high priests performing an animal sacrifice beside the First Temple illustrates the function of the room.

On Monday, the Temple Institute started preparing to build a Third Temple on Jerusalem's Mount Moriah, the site of the Dome of the Rock and the Aksa mosque, by inaugurating a workshop that manufactures priestly garments.

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No digging, please, on the Temple Mount, apart from controlled, scientific archaeological excavations. And the time is not yet right even for those.

UPDATE (12 July): More here.