As of 2020 tours from Djupivogur to Papey were stopped. If this will change i will update

Papey, a small island off Iceland's East Coast, is a haven for birdwatchers and nature lovers. Home to a large colony of Atlantic Puffins and guillemots, this uninhabited island has a rich history dating back to Irish Christian hermits and Norse settlers. The island's abandoned settlement still echoes with the remnants of its past, including the oldest wooden church in Iceland. Today, Papey offers a peaceful escape from the mainland, perfect for a day trip exploring its natural beauty and historical sites.