Along the Divan Yolu is the Köprülü kulliye (a complex around a mosque, with other facilities). This Han, at the other side of the Divan Yolu from the mosque and tombs, is part of the same kulliye. A merchant could stay the night here, and store his goods.
It's from 1659-1660, founded by Mehmet Pasha and Fazil Ahmet Pasha, both from the Köprülü family, a family that is "considered to be the most distinguished family in the whole family of the Ottoman Empire" (quote from Strolling Through Istanbul, Redhouse Press 1989). Five members of this family were Grand Vezir in the second half of the 17th century and early 18th century.
This is looking back.