Here's a more compact version of the click-through ad script using jQuery

<!-- HTML code for the ad -->
<a href="#" id="ad-link"><img src="/ad-image.jpg" alt="Advertisement"></a>

<!-- jQuery code for the ad -->
<script src="https://code.jquery.com/jquery-3.6.0.min.js"></script>
<script>
  $(document).ready(function() {
    // Add a click event listener to the ad link
    $('#ad-link').click(function(event) {
      // Prevent the default behavior of the link
      event.preventDefault();

      // Redirect the user to the ad destination URL
      window.location.href = 'https://www.example.com/ad-page';
    });
  });
</script>

In this example, we're using the jQuery library to simplify the code. The $(document).ready() function ensures that the code runs only after the page has finished loading.

The $() function is a shorthand for jQuery(), which allows us to select the ad link using its ID (#ad-link). We then add a click event listener to the selected element using the .click() method.

Inside the click event listener, we prevent the default behavior of the link using event.preventDefault(), and then redirect the user to the ad destination URL using window.location.href.