Example of creating a reusable object that provides the Drupal pager easily. See SearchResults.php for an example.

PagerService.php

<?php

namespace Drupal\velirsearch\Service;

use Symfony\Component\DependencyInjection\ContainerAwareTrait;
use Symfony\Component\DependencyInjection\ContainerAwareInterface;
use Symfony\Component\HttpFoundation\RequestStack;

class PagerService implements ContainerAwareInterface {

  use ContainerAwareTrait;

  /**
   * @var \Symfony\Component\HttpFoundation\Request
   */
  private $requestStack;

  /**
   * PagerService constructor.
   * @param \Symfony\Component\HttpFoundation\RequestStack $requestStack
   */
  public function __construct(RequestStack $requestStack) {
    $this->requestStack = $requestStack;
  }

  /**
   * {@inheritdoc}
   */
  public static function create(ContainerInterface $container) {
    $requestStack = $container->get('request_stack');
    return new static($requestStack);
  }

  /**
   * @param $totalRows
   * @param $limit
   * @return array
   */
  public function getPager($totalRows, $limit = 10) {
    pager_default_initialize($totalRows, $limit);
    return ['#type' => 'pager'];
  }
}