JSFiddle - React, Tailwind, and code Playground

HTML

<div class="select-style">

  <select>
      <option value="volvo">Please select an option</option>
    <option value="volvo">Volvo</option>
    <option value="saab">Saab</option>
    <option value="mercedes">Mercedes</option>
    <option value="audi">Audi</option>
  </select>
</div>

CSS

.select-style {
    border: 1px solid #333;
    width: auto;
    height: 32px;
    overflow: hidden;
    position: relative;
    margin: 40px;
    /* padding-top: 8px; */
}
.select-style:after {
    content: '';
    display: inline-block;
    width: 30px;
    height: 30px;
    background: #fafafa url("http://icons.iconarchive.com/icons/iconsmind/outline/128/Triangle-ArrowDown-icon.png") no-repeat 98% 4px;
    background-size: 26px 26px;
    position: absolute;
    right: 0;
    top: 0;
    pointer-events: none;
}

.select-style select {
    padding: 9px 8px 0 5px;
    width: 100%;
    border: none;
    font-size: 14px;
}

.select-style select:focus {
    outline: none;
}