JSFiddle - React, Tailwind, and code Playground

HTML

<div ng-app="app" ng-controller="MainCtrl">
    <div click aaa="aaa()" action="action()"></div>

</div>

JavaScript

var app = angular.module('app', []);

app.directive('click', function () {
    return {
        scope: {
            aaa: '&',
            action: '&'
        },
        template: 
            '<button ng-click="aaa()">show aaa (work ok)</button>' +
            '<button ng-click="action()">show bbb (not work)</button>' +
            '<br>How to pass ng-click action in variable into directive?'
    }
});
app.controller('MainCtrl', function($scope) {
    $scope.aaa = function () { alert('aaa'); }
    $scope.bbb = function () { alert('bbb'); }

    $scope.action = $scope.bbb;
});