add_action( 'admin_print_scripts', 'my_admin_term_filter', 99 );
function my_admin_term_filter() {
  $screen = get_current_screen();

  if( 'post' !== $screen->base ) return; // только для страницы редактирвоания любой записи
  ?>
  <script>
  jQuery(document).ready(function($){
    var $categoryDivs = $('.categorydiv');

    $categoryDivs.prepend('<input type="search" class="fc-search-field" placeholder="фильтр..." style="width:100%" />');

    $categoryDivs.on('keyup search', '.fc-search-field', function (event) {

      var searchTerm = event.target.value,
        $listItems = $(this).parent().find('.categorychecklist li');

      if( $.trim(searchTerm) ){
        $listItems.hide().filter(function () {
          return $(this).text().toLowerCase().indexOf(searchTerm.toLowerCase()) !== -1;
        }).show();
      }
      else {
        $listItems.show();
      }
    });
  });
  </script>
  <?php
}