There's some additional details in the film's Official Guide. In short, Dryden uses a mixture of legal and non-legal methods to acquire the items in his collection.
OBJECTS OF INTEREST
The displays in Dryden's study are only a fraction of the rarities in
his collection. Vos rotates out the galleries at whim, requesting
items from storehouses on Tanaab, Byblos, Cato Neimoidia, and
elsewhere. He employs well-paid buyers and relic-hunters to risk their
lives in order to find him new trophies.
Dryden Vos does not follow any of the regulations that prevent ethical
archaeologists from taking items sacred to other cultures. His display
of mystical antiquities includes Rafa life crystals, arks that hold
the ashes of Chancellor Contispex I, Rakatan wraith boxes, and the
Dancing Goddess idol of the Godoan people.
As to the presence of a reconditioned Sith Holocron, there's another Sith item in his collection, raided from a Sith Temple. It's possible (and in fact, downright likely) that they came from the same source.