<div class="container">
  <select>
    <option>Option 1</option>
    <option>Option 2</option>
    <option>Option 3</option>
    <option>Option 4</option>
    <option>Option 5</option>
    <option>Option 6</option>
  </select>
</div>

.container {
  display: inline-block;
  min-width: 400px;
  position: relative;
}
.container::after {
  border: 5px solid transparent;
  border-top-color: #aaa;
  content: '';
  display: inline-block;
  height: 0;
  pointer-events: none;
  position: absolute;
  right: 12px;
  top: calc(50% + 4px);
  transform: translateY(-50%);
  width: 0;
}

select {
  -moz-appearance: none;
  -webkit-appearance: none;
  appearance: none;
  background-color: #fff;
  border: 1px solid #ced4da;
  border-radius: .25rem;
  color: #495057;
  cursor: pointer;
  display: inline-block;
  font-size: 1rem;
  font-weight: 400;
  line-height: 1.5;
  padding: .375rem 1.75rem .375rem .75rem;
  vertical-align: middle;
  width: 100%;
}