<div class="cp_ipselect01">
  <select required>
    <option value="" hidden>Choose</option>
    <option value="1">cat</option>
    <option value="2">dog</option>
    <option value="3">rabbit</option>
    <option value="4">squirrel</option>
  </select>
</div>

.cp_ipselect01 {
  position: relative;
  display: flex;
  align-items: center;
  margin: 2em auto;
  border: 1px solid #bbbbbb;
  border-radius: 2px;
}
/*プルダウンの三角を設定*/
.cp_ipselect01::before {
  position: absolute;
  right: 15px;
  content: '';
  width: 16px;
  height: 8px;
  background: #666666;
  clip-path: polygon(0 0, 100% 0, 50% 100%);
}
.cp_ipselect01 select {
  width: 100%;
  padding: 10px 45px 10px 10px;
  color: #666666;
  cursor: pointer;
  text-overflow: ellipsis;/*テキストがオーバーしたら'...'で省略*/
  z-index: 1;
  /* 標準のスタイルを無効にする */
  border: none;
  appearance: none;
  outline: none;
  background: transparent;
}