You have to check the status of TK 1683 to FCO when you land. There are big screens everywhere. There is theoretical chance that you can make it to the gate before it closes, in particular if the flight is delayed. If no delay, the chance is slim as your flight is expected to land at shortly before 5PM.

Do keep in mind that there are 3 flights to FCO tomorrow. You don't have to get rebooked to the first flight tomorrow morning; you can ask for later if you prefer to get more sleep at the hotel and a few hours to explore Istanbul before heading to airport tomorrow.