" Is there an equivalent in the Orthodox church?"
Not that I am aware of. Kosta?
Kolokotronis: Not that I am aware of. Kosta?
No, there is no "depository of faith" or magistrarium. Orthodoxy is based on a firm belief that the faith once delivered by the Apostles is complete and immutable, just like God Himself, Who gave it to us.
In other words, we may not "discover" more, or add to the faith we have been given (for reasons of current "reality" or political "correctness" or modern trends, or whatever other human reasons); our premise is that the Apostles and their successors believed in one and the same thing and that their knowledge of God was no different than ours. No change! No additions! No innovations! Only explanations.