Edit in JSFiddle

//created for this example function
function addButton(){

   var button=document.createElement("button");
   button.innerText="Click me!";
   document.querySelector("#parent").appendChild(button);
   
   return button;
};

//binding addButton
document.querySelector("#add").addEventListener("click",function(){

   bindButton(addButton());//every time we add - we must bind it

});


//standard event binding
function bindButton(button){

   button.addEventListener("click",function(){
   
        print("Button was clicked. Standard event listener.");
   
   });

};

//bind button on start
bindButton(document.querySelector("#parent button"));

<div id="parent">
<button>
Click me!
</button>
</div>
<button id="add">
Add Click button
</button>