JSFiddle - React, Tailwind, and code Playground

HTML

<div>
  <ul>
    <li>Item1  <a class="moveUp">Move Up</a> <a class="moveDown">Move Down</a></li>
    <li>Item2  <a class="moveUp">Move Up</a> <a class="moveDown">Move Down</a></li>
    <li>Item3  <a class="moveUp">Move Up</a> <a class="moveDown">Move Down</a></li>
    <li>Item4  <a class="moveUp">Move Up</a> <a class="moveDown">Move Down</a></li>
    <li>Item5  <a class="moveUp">Move Up</a> <a class="moveDown">Move Down</a></li>
  </ul>
</div>

JavaScript

$('ul').on('click', 'a', function(){
    var $this = $(this),
        $li = $this.parent();
    
    if ($this.hasClass('moveUp') &&  $li.prev().length>0){
        $li.prev().before($li[0]);
    }
    else if ($this.hasClass('moveDown') && $li.next().length>0){
        $li.next().after($li[0]);
    }
});