const origSelect = document.querySelector('select');
const options = [...origSelect.options];
origSelect.addEventListener('change', () => {
  options.forEach(option => option.removeAttribute('selected'));
  options[origSelect.selectedIndex].setAttribute('selected', '');
});

function cloneIt() {
  let newFields = document.getElementById('clonedFields');
  let cloneThis = document.getElementById('cloneThis');
  let clonedNode = cloneThis.cloneNode(true);
  clonedNode.querySelector('select').value = origSelect.value;
  newFields.parentNode.appendChild(clonedNode);
}

<div id="cloneParent">
  <div id="cloneThis">
    <select id="cloneTestSelect">
      <option value="Option1">Option1</option>
      <option value="Option2">Option2</option>
      <option value="Option3">Option3</option>
      <option value="Option4">Option4</option>
    </select>
    <label for="cloneTestText">Text Input: </label>
    <input type="text" id="cloneTestText">
    <label for="cloneTestNumber">Number Input: </label>
    <input type="text" id="cloneTestNum">
  </div>
</div>
<br>
<h1>Cloned fields: </h1>
<br>
<div id="clonedFields"></div>
<button onclick="cloneIt()">Clone inputs</button>

const origSelect = document.querySelector('select');

function cloneIt() {
  let newFields = document.getElementById('clonedFields');
  let cloneThis = document.getElementById('cloneThis');
  let clonedNode = cloneThis.cloneNode(true);
  clonedNode.querySelector('select').value = origSelect.value;
  newFields.parentNode.appendChild(clonedNode);
}

<div id="cloneParent">
  <div id="cloneThis">
    <select id="cloneTestSelect">
      <option value="Option1">Option1</option>
      <option value="Option2">Option2</option>
      <option value="Option3">Option3</option>
      <option value="Option4">Option4</option>
    </select>
    <label for="cloneTestText">Text Input: </label>
    <input type="text" id="cloneTestText">
    <label for="cloneTestNumber">Number Input: </label>
    <input type="text" id="cloneTestNum">
  </div>
</div>
<br>
<h1>Cloned fields: </h1>
<br>
<div id="clonedFields"></div>
<button onclick="cloneIt()">Clone inputs</button>