Pass argument when overriding controller in RouteSubscriber
Actually, I have found an error in my code.
Everything works normally, when the param name and type are set properly.
So the final code should be:

My sample page controller is this:

&lt;?php

namespace Drupal\my_module\Controller;

use Drupal\Core\Controller\ControllerBase;
use Symfony\Component\DependencyInjection\ContainerInterface;
use Drupal\taxonomy\TermInterface;

/**
 * Class PagerController.
 */
class PagerController extends ControllerBase {

  /**
   * Handlepage.
   *
   * @return string
   *   Return Hello string.
   */
  public function handleDefaultPage(TermInterface $taxonomy_term) {
    return [
      '#type' =&gt; 'markup',
      '#markup' =&gt; 'term: ' . $taxonomy_term-&gt;getName(),
    ];
  }
}


And its routing is this:

my_module.pager_controller_handleDefaultPage:
  path: '/taxonomy/term/{taxonomy_term}'
  defaults:
    _controller: '\Drupal\my_module\Controller\PagerController::handleDefaultPage'
    _title: 'Taxonomy Pager'
  requirements:
    _permission: 'access content'
    _entity_access: 'taxonomy_term.view'
    taxonomy_term: \d+