JSFiddle - React, Tailwind, and code Playground

HTML

<span class="select">
    <select>
        <option>A</option>
        <option>B</option>
    </select>
</span>

CSS

body {
    background:#eef;
    font-family:sans-serif;
}
.select {
    display:inline-block;
    background-color:#fff;
    border-radius:.5em;
    border:.1rem solid #000;
    color:#013;
    width:8em;
    height:1.5em;
    vertical-align:middle;
    position:relative;
}
.select:after {
    position:absolute;
    bottom:.15em;
    top:.15em;
    right:.5rem;
    content:'\2193';
    pointer-events: none;
}
select {
    -webkit-appearance:none;
    -moz-appearance:none;
    appearance:none;
    font:inherit;
    border:none;
    background-color:transparent;
    color:inherit;
    width:100%;
    height:100%;
    padding:0 .5em;
}