Hi
@Mustafa Umut Sarac
What you will need to do is technically over develop your negative for a stop. The timings for any developer is well published and you can use Massive Dev Chart to find the developer/film combination. The purpose of over developing is giving a bit more contrast to the negative but as others have said, that will in fact effect the entire roll. When AA and others have developed Zone System, they were mainly focused on sheet films where each sheet of film was developed individually to have more control on the print. Because the films, papers and developers were more limited, as what they can produce etc., they were trying to compensate for what they have in hand. Another use of over developing is to compensate for under exposing, such as you expose your film with less light, rating a ISO400 film as ISO800. Overdeveloping will effect the shadow areas less and will effect highlight areas more so ideally, you need to balance that somehow as well. Otherwise your negatives will be too contrasty.
Also, although it is not a must, you would need ideally a spot meter to use ZS effectively, that is to measure a particular area of the scene and put that scene into one of the zones on the chart, between 0 to 10. When we use incident meters, that measures Zone V and we measure the light which falls on our subject, like a face on the portrait. When you use a spot or reflective meter, then you need to know what reflection of the subject has and then put that accordingly, ie if you measure a white person technically that measurement needs to fall in Zone VI and if you take a measurement from darker skin person, that needs to be put on Zone IV or Zone III depending the skin color.
As how you can understand a true N+1 development, if you develop yourself, more or less that is 10-15% longer development. If you are giving to a lab then you'll ask them to push (itme) for a stop. Now I am not entirely sure if labs in Istanbul will do that for you as I have not heard great stories about them, however certain ones are still operating well.
My personal recommendation is, if you use only 35mm film, expose the entire roll same way, and develop the entire roll same way without going into Zine System as you cannot control each frame individually. If you shoot sheet or 120 films then you have a bit more chance, although 120film still has 8 to 16 frames, at least by changing backs you can have more flexibility in case you have such a camera.