JSFiddle - React, Tailwind, and code Playground

HTML

<select name="start_time">
</select>

<select name="end_time">
  <option value="default">Pick a start time</option>
</select>

JavaScript

// Add each option to start_times
for (var hour = 9; hour <= 21; hour++) {
  var option = "<option value='"+hour+"'>"+hour+"</option>";
	$('[name="start_time"]').append(option);
}

// When the start time is changed, set the end time
$('[name="start_time"]').on('change', function() {
	// This is the start time chosen
  var start_time = $(this).val();
  // Remove the default option
  $('[name="end_time"]').find('option').remove();
  // Add options after the start time
  for (var hour = parseInt(start_time) + 1; hour <= 24; hour++) {
	  var option = "<option value='"+hour+"'>"+hour+"</option>";
    $('[name="end_time"]').append(option);
  }
});