No,.... don't use static anything, neither methods nor fields because if you do this, you'll break object-oriented programming rules, leaving your code difficult to update and maintain. The exception of course would be your main method, and carefully chosen fields and methods who truly belong to the class. Instead give the class that needs to call the Element object's method a valid reference to the object whose state you wish to change, the drawing JPanel or Element object. This can be done by passing in a valid reference via a constructor parameter.
public class Listener extends AbstractAction {
private Elements elements;
public Listener(Elements elements) {
this.elements = elements;
}