JSFiddle - React, Tailwind, and code Playground

HTML

<label class="select">
    <select class="select__control">
        <option>aaaa1</option>
        <option>aaaa2</option>
        <option>aaaa3</option>
        <option>aaaa4</option>
        <option>aaaa5</option>
        <option>aaaa6</option>
    </select>
    <span class="select__icon">i</span>
</label>

CSS

.select {  
  display: block;
  overflow: hidden;
  height: 40px;
  width: 100%;
  position: relative;
  font-size: 16px;
}

.select__control {
  height: 40px;
  padding: 5px;
  border: 0;
  border: 1px solid #ccc;
  width: 100%;
  -webkit-appearance: none;
  appearance: none;
  box-sizing: border-box;
}

.select__icon{
  position: absolute;
  right: 0;
  top: 0;
  width: 40px;
  height: 40px;
  display: flex;
  align-items: center;
  justify-content: center;
  background-color: #00f;
  color: #fff;
  pointer-events: none;
  box-sizing: border-box;
}