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(){

   addButton();//add button

});

document.querySelector("#parent").addEventListener("click",function(e){

   if (e.target.tagName=="BUTTON"){
      
       print("Button was clicked. Delegated event listener.");
   }

});

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