JSFiddle - React, Tailwind, and code Playground

HTML

<div class="form-group">
  <label for="priority">Task priority</label><br>
    <div class="selectorDiv">
      <select class="form-control selectElement" style="width:480px; appearance: none;">
        <option value="urgent" selected="selected">Urgent</option>
        <option value="important">important</option>
        <option value="later">Later</option>
      </select>
    </div>
  </div>
</div>

CSS

.selectElement
{
  -moz-appearance: none;
  -webkit-appearance: none;
  appearance: none;
  
  height:50px;
  
  /* Your style */
  border:0 !important;
  outline:none !important;
  color:black;
  -moz-box-shadow: 0 0 3px #ccc;
  -webkit-box-shadow: 0 0 3px #ccc;
  box-shadow: 0 0 3px #ccc;
  /* padding:20px !important; */
  height: 43px !important;
  border-radius:4px !important;  

}

.selectorDiv
{
  position:relative;
  display: inline-block;
}

.selectorDiv::before
{
  position: absolute;
  right: 20px;
  top:0;
  bottom:0;
  
  margin-top:auto;
  margin-bottom:auto;
  
  margin-left: auto;
 
  content: "";
  z-index:5;
  
  width: 0; 
  height: 0; 
  border-top: 10px solid transparent;
  border-bottom: 10px solid transparent;
  
  border-left: 10px solid green;  
  
  pointer-events:none;
  
}