Add onclick with css pseudo-element after

Is it possible in my css file to do something like [see code above]?

No

The important question to ask is why.

HTML has control of the data within the webpage. Any CSS or JS is specified via the HTML. It's the Model.

CSS has control of the styles, there is no link between CSS and HTML or JavaScript. It's the View.

JavaScript has control of the interactions within the webpage, and has hooks to any and all DOM nodes. It's the Controller.

Because of this MVC structure: HTML belongs in .html files, CSS belongs in .css files, and JS belongs in .js files.

CSS pseudo-elements do not create DOM nodes. There is no direct way for JavaScript to access a pseudo-element defined in CSS, and there's no way to attach an event to said pseudo-elements.

If you've got a set structure in place, and can't add the additional content necessary to produce new links within the HTML, JavaScript can dynamically add the new elements necessary which can then be styled via CSS.

jQuery makes this very simple:

$('<span class="click-me">click me</span>').appendTo('.myclass').click(my_function);

Well,

using expression it might actually be possible for internet explorer only.

Otherwise:

No. Not at all, that's not what css is made and intended for.

If something can be done with jQuery, then it is sure that it is possible to do it without that. Lets see a data model:

<div id="container"><div id="hasblock" onclick='clickFunc(this, event)'></div></div>

We need some stylesheet:

<style>div#container { width:100px; height:50px;position relative; border:none;}div#hasblock {width:100px; height:50px;position absolute;border:solid black;}div#hasblock::after {content:"Click me"; position: absolute; border:solid red;top:80px;left:0px;display:block;width:100px;height:20px; font-size:18px;}</style>

And a code:

<script>function clickFunc(his, event){if (event.clientY>his.clientHeight){console.log("It was a click");};    }</script>