Вариант.
<select>
<option value="2000">2000</option>
<option value="2001">2001</option>
<option value="2002">2002</option>
<option value="2003">2003</option>
<option value="2004">2004</option>
<option value="2005">2005</option>
<option value="2006">2006</option>
<option value="2007">2007</option>
<option value="2008">2008</option>
<option value="2009">2009</option>
<option value="2010">2010</option>
<option value="2011">2011</option>
<option value="2012">2012</option>
<option value="2013">2013</option>
<option value="2014">2014</option>
<option value="2015">2015</option>
<option value="2016">2016</option>
<option value="2017">2017</option>
<option value="2018">2018</option>
<option value="2019">2019</option>
<option value="2020">2020</option>
</select>
<select>
<option value="2000">2000</option>
<option value="2001">2001</option>
<option value="2002">2002</option>
<option value="2003">2003</option>
<option value="2004">2004</option>
<option value="2005">2005</option>
<option value="2006">2006</option>
<option value="2007">2007</option>
<option value="2008">2008</option>
<option value="2009">2009</option>
<option value="2010">2010</option>
<option value="2011">2011</option>
<option value="2012">2012</option>
<option value="2013">2013</option>
<option value="2014">2014</option>
<option value="2015">2015</option>
<option value="2016">2016</option>
<option value="2017">2017</option>
<option value="2018">2018</option>
<option value="2019">2019</option>
<option value="2020">2020</option>
</select>
<script>
let [s1, s2] = document.querySelectorAll("select"),
fragment = document.createDocumentFragment();
s1.addEventListener("change", e => {
let val = s2.value;
for (let x of e.target.options){
x.value >= e.target.value && fragment.appendChild(x.cloneNode(true));
}
s2.options.length = 0;
s2.appendChild(fragment);
val > e.target.value && (s2.value = val);
});
</script>