How to add pagination to comments?

Put below code into your current theme’s comments.php file:

<div class="navigation">
    <?php paginate_comments_links(); ?> 
</div>

<ol class="commentlist">
    <?php wp_list_comments(); ?>
</ol>

<div class="navigation">
    <?php paginate_comments_links(); ?> 
</div>

This code will display pagination as you expect. Don’t forgot to check the break comment to part with number of settings from Admin > Settings > Discussion Settings. See below example snap.

I tested this code and this should work for you also. You can check more detail about paginate_comments_links here.