How to call directive from controller function [AngularJS]

You have a few choices to go the way you want. If I were you, I would instead move your AJAX call into your directive to sidestep the issue entirely (even better: move the AJAX call to a service that gets injected into the directive):

angular.module('app').directive('directive', [
    '$http',
    function($http) {
        return {
            link: link,
            scope: {}
        };

        function link(scope, elem, attrs) {
            scope.doAjax = doAjax;

            function doAjax() {
                $http.get('url').then(function() {
                    elem.append('<p>success</p>');
                });
            }
        }
    }
]);

If you absolutely have to have the AJAX call in your controller, you can use events, but you should be sparing with these as they will clog up the digest loop:

// Controller
function doAjax() {
    $http.get('url').then(function() {
        $scope.$broadcast('some.event.descriptor');
    });
}

// Directive
function link(scope, elem, attrs) {
    scope.$on('some.event.descriptor', function() {
        elem.append('<p>success</p>');
    });
}

Another option you have is to bind some data from the controller to your directive:

// Controller
$scope.someData = '';
$http.get('url').then(function() {
    $scope.someData = 'success';
});

<!-- Controller Template -->
<directive data-something="someData"></directive>

// Directive
function() {
    return {
        scope: {
            something: '='
        }
    };
}

<!-- Directive Template -->
<p>{{ something }}</p>