JSFiddle - React, Tailwind, and code Playground

HTML

<div class="select">
  <select>
    <option value="">Seleccione uno:</option>
    <option value="opcion-1">Opción 1</option>
    <option value="opcion-2">Opción 2</option>
    <option value="opcion-n">Opción N</option>
  </select>
</div>

CSS

.select {
  position: relative;
  border: 1px solid #ccc;
  width: 120px;
  height: 20px;
  line-height: 20px;
  margin: 50px auto 10px;
  overflow: hidden;
  background-color: #fff;
}
  .select:before {
    content: '';
    position: absolute;
    right: 5px;
    top: 7px;
    width: 0;
    height: 0;
    border-style: solid;
    border-width: 7px 5px 0 5px;
    border-color: #000000 transparent transparent transparent;
    z-index: 5;
    pointer-events: none;
  }
  .select select {
    padding: 5px 8px;
    width: 130%;
    border: none;
    box-shadow: none;
    background-color: transparent;
    background-image: none;
    appearance: none;
  }