Custom pagination (Title, date and teaser)

I assume you’re talking about single posts, not archives – get_next_posts_link gets the next archive page, get_next_post_link gets the post next to the current one (note the plural difference).

If so, the next/previous post link functions are just wrappers for get_adjacent_post():

<?php if ( $the_query->max_num_pages > 1 ) : ?>

    <nav class="prev-next-posts">
        <?php if ( $post = get_adjacent_post( false /* In same term? */, '' /* Excluded terms */, true /* Previous */ ) ) : setup_postdata( $post ) ?>

            <div class="prev-posts-link">
                <a href="https://wordpress.stackexchange.com/questions/208091/<?php the_permalink() ?>"><?php the_title() ?></a>

                <?php the_excerpt() ?>
            </div>

        <?php endif ?>

        <?php if ( $post = get_adjacent_post( false, '', false ) ) : setup_postdata( $post ) ?>

            <div class="next-posts-link">
                <a href="https://wordpress.stackexchange.com/questions/208091/<?php the_permalink() ?>"><?php the_title() ?></a>

                <?php the_excerpt() ?>
            </div>

        <?php endif ?>

        <?php wp_reset_postdata() ?>
    </nav>

<?php endif ?>