I have developed a Tkinter GUI and need to add a button in the GUI window top panel, next to the minimise, maximise and close buttons. The button then calls a function. How can this be done?
Tkinter doesn't have any support to do what you want. You'll have to find some sort of platform-specific library to alter what is shown in the window border. 
Your only other option is to turn off the window border provided by your OS with overrideredirect, and then create your own border with whatever controls you want. This requires a lot of work because you also have to write the code for moving and resizing the window, but it's possible.
Add button to Tkinter Window panel before minimise, maximise buttons