Koca Sinan Paşa complex aka Sinan Paşa complex
From elsewhere on the web (website findagrave) and the GPS-coordinates of the pictures I understood this is the Sinan Pasha türbe (the high building) with a sebil (spot where water was distributed, now a shop with fruit and such).

The Koca Sinan Paşa Complex is located on Yeniçeriler Street at Çarsikapi between Çemberlitaş and Beyazit Squares.

Built in 1593, the complex consists of the tomb of Koca Sinan Paşa, a madrasa and a sebil clustered inside a small and irregular walled-in precinct with grilled windows along its walls. The precinct is entered from two main gates located on Yeniçeriler Street -the continuation of Divanyolu, or the main route of the historic peninsula- to the south and Bileyciler Street, which meets Yeniçeriler Street at a narrow angle to the west. On this wedge-shaped irregular site that slopes down towards the main route, the sabil is placed projecting at the tip facing both streets and the tomb rises immediately behind it. The madrasa and its adjoining classroom occupy higher ground to the east. All the buildings are aligned with Yeniçeriler Street to the south.

The tomb of Koca Sinan Pasa is a sixteen-sided domed structure, preceded by a gable-roofed portico to the west. Entering the precinct from Yeniçeriler Street, the tomb entrance is seen on the left and a small cemetery, created in the eighteenth century, is set on a terrace across from it. A short pathway passes underneath the tomb portico and leads up the stairs to the terrace level. To the left, a gate leads out to Bileyciler Street. To the right, is the madrasa classroom, which is preceded by a three-bay portico facing south.

The Koca Sinan Pasa complex is a notable example of Ottoman classical architecture: its buildings have precise geometrical proportions and are subtly decorated with polychrome stone and stalactites.
In 2015 I found it almost finished after a restoration.