One simple and direct approach is to do what you always do when you want to reuse functionality: Make it a function you can call from more than one place:
// The original handler
function originalHandler() {
alert('I was clicked');
}
// Hooking it up, not including the special element
$('.element:not(.specific_extended_element)').click(originalHandler);
// Hooking up your additional handler
$('.element.specific_extended_element').click(function(e){
alert('Extended click');
originalHandler.call(this, e);
});