Вы можете использовать метод trace
на вашем StringVar
.
def __init__(self,master):
self.master = master
self.var = StringVar()
self.var.trace("w", self.openFileCurrentDir)
l = ["A","B","C","D"]
self.fileOptionMenu = OptionMenu(self.master, self.var, *l)
self.fileOptionMenu.pack()
def openFileCurrentDir(self,*args):
print("inside openFileCurrentDir()"+self.var.get())