In fact you have already answered your question in your own message.

After court decreed that he owns you some money, if he doesnt pay it at will, you appeal to a public authority (called "İcra") to "force" him to pay you. If he does not, this authority confiscates his assets, sells them in auctions and pays you. (This process is also called "icra").

What "İcra" will pay you is the amount of money the court decreed (and interest and some "icra" expenses). You'll get a small fee for having a lawyer, but this is no way on par with what you paid to your lawyer, so practically answer is no, you will not get lawyer fee.