JSFiddle - React, Tailwind, and code Playground

HTML

<select class="a">
  <option>1</option>
  <option>2</option>
  <option>3</option>
</select>

<select class="b">
  <option>1</option>
  <option>2</option>
  <option>3</option>
</select>

CSS

select {
  display: block;
  margin-top: 30px;
  background-image: url(https://i.imgsafe.org/246e8ff.png);
  background-repeat: no-repeat;
  background-position: 100% 0%;
  width: 100px;
  height: 30px;
  -webkit-appearance: none;
  -moz-appearance: none;
  border: 1px solid black;
  font-size: 14px;
}

select::-ms-expand {
  display: none;
}

.b {
  border-radius: 20px;
}