JSFiddle - React, Tailwind, and code Playground

HTML

Native:
<select>
    <option value="1">Option 1</option>
    <option value="2">Option 2</option>
</select>
<div></div>
Styled no SVG:
<span class="select nosvg">
<select>
    <option value="1">Option 1</option>
    <option value="2">Option 2</option>
</select>
</span>
<div></div>
Styled with SVG:
<span class="select svg">
<select>
    <option value="1">Option 1</option>
    <option value="2">Option 2</option>
</select>
    <svg class="button">v</svg>
</span>

CSS

.select
{
    position: relative;
}

.select.svg > .button
{
    position: absolute;
    top: 0;
    right: 0;
    width: 16px;
    height: 19px;
    background: red;
    content: "";
    pointer-events: none;
}

.select.nosvg:after
{
    position: absolute;
    top: 0;
    right: 0;
    width: 16px;
    height: 19px;
    background: red;
    content: "";
    pointer-events: none;
}