JSFiddle - React, Tailwind, and code Playground

HTML

<p>
  <select class="classic">
      <option value="Vancouver Island University">University of Arizona</option>
      <option value="Western University">University of B</option>
      <option value="Wilfrid Laurier University">University of C</option>
      <option value="York University">University of D</option>
   </select>

</p>

CSS

select {
  background-color: white;
  border: thin solid blue;
  border-radius: 4px;
  display: inline-block;
  font: inherit;
  line-height: 1.5em;
  padding: 0.5em 3.5em 0.5em 1em;
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
  -webkit-appearance: none;
  -moz-appearance: none;
}
select.classic {
  background-image:    url('data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAYCAYAAADgdz34AAAA3klEQVRIS+3VMU9CMRTF8d8zBL+aizoQFhx0kUk33RzdYMNFXUFnYeGrYYyaJiUxJHDLSxodbNKpfeffc9/pbaPyaCrr+3OA++z4rtT5Pg5GuMnCY9yWQEoBE1xhlUUP8YDrCBIB0vojLvGO0yz4hm4JJAKcYYoPHGOZAUdYoIMBXrc5iQAHeMlzviFygj7O8dkWEJU4XI8chALRhn9AVKHf70VRTHu4wFfbmKZLNKt50dLBnna0imcMd/2I0phWa3Y/D1e1Xa9BCZJG0VuQNpaWKMx72xS1Fl5/WN3BN+AgJhnZQlq4AAAAAElFTkSuQmCC');
  background-position: calc(100% - .5rem), 100% 0;
  background-size:  1.5em 1.5em;
  background-repeat: no-repeat;
}

select.classic:focus {
  background-image: url('data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAYCAYAAADgdz34AAAA3klEQVRIS+3VMU9CMRTF8d8zBL+aizoQFhx0kUk33RzdYMNFXUFnYeGrYYyaJiUxJHDLSxodbNKpfeffc9/pbaPyaCrr+3OA++z4rtT5Pg5GuMnCY9yWQEoBE1xhlUUP8YDrCBIB0vojLvGO0yz4hm4JJAKcYYoPHGOZAUdYoIMBXrc5iQAHeMlzviFygj7O8dkWEJU4XI8chALRhn9AVKHf70VRTHu4wFfbmKZLNKt50dLBnna0imcMd/2I0phWa3Y/D1e1Xa9BCZJG0VuQNpaWKMx72xS1Fl5/WN3BN+AgJhnZQlq4AAAAAElFTkSuQmCC');
  background-position: calc(100% - .5rem), 100% 0;
  background-size:  1.5em 1.5em;
  background-repeat: no-repeat;
  border-color: grey;
  outline: 0;
}