This gate, and the long calligraphic inscription on it, date from 1798-1800, when the Eyüp Sultan Mosque was rebuilt in Turkish Baroque style; the original mosque (1459) had collapsed due to an earthquake in 1766.
Above the inscription stands the ‘tuğra’ of Selim III, who had the mosque rebuilt.

A ‘tuğra’ is a calligraphic monogram, seal or signature of an Ottoman sultan, that was affixed to all official documents and correspondence. It was also carved on his seal and stamped on the coins minted during his reign. Each sultan generally chose the precise form of his ‘tuğra’ on the day of his accession from specimens prepared for him in advance by the court calligrapher. The first ‘tuğra’ belonged to Orhan I (1284–1359), the second ruler of the Ottoman Empire and it evolved until it reached the classical form in the ‘tuğra’ of Sultan Suleiman the Magnificent (1494–1566).

Correspondent: J.M.Criel, Antwerpen.
Sources: ‘Türkiye Tarihi Yerler Kılavuzu’ – M.Orhan Bayrak, Inkılâp Kitabevi, Istanbul, 1994 & Wikipedia.