The Ottoman Imperial Archives does not identify Tanburi Isak as a Jew.
But, there's something about the portrait (photography did not exist in his day). Maybe it is his name Isak, maybe his beard, maybe his turban which is similar to the one still worn by Sephardi chief rabbis of Israel. Research proved the hunch correct.
Tamburi/Tanburi İsak Efendi (1745-1814)