Дело в том, что вы находитесь в детской области действия, созданной UI-Bootstrap.
Если вы действительно хотите это сделать - единственный способ получить к нему доступ через $parent
следующее должно работать
<!doctype html>
<html ng-app="ui.bootstrap.demo">
<head>
<script src="//ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular.js"></script>
<script src="//ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular-animate.js"></script>
<script src="//ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular-sanitize.js"></script>
<script src="//angular-ui.github.io/bootstrap/ui-bootstrap-tpls-2.5.0.js"></script>
<script src="example.js"></script>
<link href="//netdna.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet">
</head>
<body>
<div ng-controller="AccordionDemoCtrl">
<script type="text/ng-template" id="group-template.html">
<div class="panel-heading">
<h4 class="panel-title" style="color:#fa39c3">
<a href tabindex="0" class="accordion-toggle" ng-click="$parent.showAlert(); toggleOpen();" uib-accordion-transclude="heading">
<span uib-accordion-header ng-class="{'text-muted': isDisabled}">
{{heading}}
</span>
</a>
</h4>
</div>
<div class="panel-collapse collapse" uib-collapse="!isOpen">
<div class="panel-body" style="text-align: right" ng-transclude></div>
</div>
</script>
<uib-accordion close-others="oneAtATime">
<div uib-accordion-group class="panel-default" heading="Custom template" template-url="group-template.html">
Hello
</div>
</uib-accordion>
</div>
</body>
</html>
И ваш JS
angular.module('ui.bootstrap.demo', ['ngAnimate', 'ngSanitize', 'ui.bootstrap']);
angular.module('ui.bootstrap.demo').controller('AccordionDemoCtrl', function ($scope) {
$scope.oneAtATime = true;
$scope.groups = [
{
title: 'Dynamic Group Header - 1',
content: 'Dynamic Group Body - 1'
},
{
title: 'Dynamic Group Header - 2',
content: 'Dynamic Group Body - 2'
}
];
$scope.items = ['Item 1', 'Item 2', 'Item 3'];
$scope.showAlert = function()
{
alert('Hello');
};
$scope.addItem = function() {
var newItemNo = $scope.items.length + 1;
$scope.items.push('Item ' + newItemNo);
};
$scope.status = {
isCustomHeaderOpen: false,
isFirstOpen: true,
isFirstDisabled: false
};
});