Event Click in ComboBox Icon

I need to run a process to make a User click on the icon of the combo box:

ComboBox MyCombo = new comboBox ("User");
myCombo.setIcon (FontAwesome.PENCIL);

How to trigger an event when give a click on PENCIL ICON?

I would recommend to split the functionality into two components in this case. Instead of setting icon for combobox, create a button and set icon for the button. That way you can set up click listener for the button in regular fashion. If you need to wrap these two together, it is simply done by putting them both in CSSLayout out and create custom class for the combined component. If you do not like button looking like regular button, you can style it so that only icon is viewed etc.