We can add/remove active class while click on menu item in jQuery. Here is the example of html, css & jquery code.

<!-- html starts -->

<ul class="navbar vertical__menu">
  <li>
    <a class="vertical__navbar-link active" href="#">navbar item 1</a>
  </li>
  <li>
    <a class="vertical__navbar-link" href="#">navbar item 2</a>
  </li>
  <li>
    <a class="vertical__navbar-link" href="#">navbar item 3</a>
  </li>
</ul>

<style>
  .navbar .navbar-link {
    color: blue
  }
  .navbar .navbar-link.active {
    color: red    
  }
</style>

<!-- google jquery cdn link -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<script>
  $(document).ready(function () {
    $('.vertical__navbar-link').click(function () {
      $('.vertical__navbar-link').removeClass("active");
      $(this).addClass("active");
    });
  });
</script>

<!-- html end -->