There are more than one way to reach the Sultanahmet region from Istanbul Airport.
Istanbul Airport to Sultanahmet Public Transportation
There are 2 alternatives in this option, but neither of them travel directly from Istanbul Airport to the Sultanahmet region.
A- HVIST-10 HAVAİST SHUTTLE BUSES + T1 TRAM
Take bus number HVIST-10 from the airport transportation floor and get off at the last stop, Aksaray Metro. Then walk to Yusufpaşa tram station and take the Bağcılar – Kabataş T1 tram (direction Kabataş) and finally get off at the Sultanahmet Square stop of the tram.