How can I dynamically add a directive in AngularJS?

In addition to perfect Riceball LEE's example of adding a new element-directive

newElement = $compile("<div my-directive='n'></div>")($scope)
$element.parent().append(newElement)

Adding a new attribute-directive to existed element could be done using this way:

Let's say you wish to add on-the-fly my-directive to the span element.

template: '<div>Hello <span>World</span></div>'

link: ($scope, $element, $attrs) ->

  span = $element.find('span').clone()
  span.attr('my-directive', 'my-directive')
  span = $compile(span)($scope)
  $element.find('span').replaceWith span

Hope that helps.

You have a lot of pointless jQuery in there, but the $compile service is actually super simple in this case:

.directive( 'test', function ( $compile ) {
  return {
    restrict: 'E',
    scope: { text: '@' },
    template: '<p ng-click="add()">{{text}}</p>',
    controller: function ( $scope, $element ) {
      $scope.add = function () {
        var el = $compile( "<test text='n'></test>" )( $scope );
        $element.parent().append( el );
      };
    }
  };
});

You'll notice I refactored your directive too in order to follow some best practices. Let me know if you have questions about any of those.