.after () jquery in JS Pure?

Use insertAdjacentHTML(posição, conteúdo) (support) :

A posição is defined relative to the element by the following types:

• "afterbegin" : Within the element, before its first child ( childNode ).
• "afterend" : After the element itself.
• "beforebegin" : Before the element itself.
• "beforeend" : Within the element, after its last child ( childNode ).

And the placement would look like:

<!-- beforebegin -->
<p>
<!-- afterbegin -->
foo 
<!-- beforeend -->
</p>
<!-- afterend -->'

conteúdo is a string to be parsed as HTML or XML and inserted into the tree.

Example:

var elemento = document.querySelector('p');
elemento.insertAdjacentHTML('afterend', '<p>Overflow</p>');

p { display: inline }

<p>Stack</p>

The jQuery function .after() inserts a sibling element later, in native javascript this is done with insertBefore() , according to the documentation:

  

( insertBefore ) Adds the specified node, before a reference element, as the child of the current node.

     

(...)

     

There is no insertAfter method. But it can be emulated by combining the insertBefore method with nextSibling .

In this way, you must insert the new node in the parent element before the next sibling element.

The short form is:

elemento.parent.insertBefore(novoElemento, elemento.nextSibling);

The code below adds a new node as it is done in the question, it is easy to understand and the comments complement.

var elementos = document.querySelectorAll('span:nth-child(3)');
var elemento, pai, div;
for (var i = 0; i < elementos.length; i++) {
  elemento = elementos[i];
  pai = elemento.parentNode;
  div = document.createElement('div');
  div.style.clear = 'both';
  // insere no elemento pai, antes do próximo irmão
  pai.insertBefore(div, elemento.nextSibling)
  // se o segundo parâmetro é nulo será inserido como último filho
}

// se for apenas um elemento utilize a linha abaixo
// e apague o loop for
var elemento = document.querySelector('li:nth-child(3)');

<span>item</span>
<span>item</span>
<span>item</span>
<span>item</span>