Wrap an X amount of taxonomy posts in a separate Row in WordPress

This should get you pretty close. The key is to use iterating loops and check which iteration you’re on to determine whether or not to output a new <div class="row">, open or close a <ul>, etc.

Note that one you are in a loop, you can just use the_permalink() and the_title() because the query already grabbed them, no need to echo get_the_title() etc.

<div class="clientsListRow"><?php 
    $post_type="clients";
    $taxonomies = get_object_taxonomies(array('post_type' => $post_type));
    foreach($taxonomies as $taxonomy) :
        $terms = get_terms($taxonomy);
        for($t=1; $t<=count($terms); $t++) {
            // if "t" is 1 or a multiple of 7, start a new row
            if($t == 1 || $t%7 == 0) { ?><div class="row"><?php }
                // if "t" is 1 or a multiple of 4, start a new list
                if($t == 1 || $t%4 == 0) { ?><ul><?php } ?>
                <li>
                    <a href="https://wordpress.stackexchange.com/questions/262224/<?php echo get_term_link($term->term_id); ?>"><?php echo $term->name; ?></a>
                    <?php
                    $args = array(
                        'post_type' => $post_type,
                        'posts_per_page' => -1,  //show all posts
                        'tax_query' => array(
                            array(
                                'taxonomy' => $taxonomy,
                                'field' => 'slug',
                                'terms' => $term->slug,
                            )
                        )
                    );
                    $posts = new WP_Query($args);
                    if($posts->have_posts()) : ?>
                        <ul>
                        <?php while($posts->have_posts() ) : $posts->the_post(); ?>
                            <li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
                        <?php endwhile; ?>
                        </ul>
                    <?php endif; ?>
                </li>
            <?php // if "t" is a multiple of 3, or the very last item, close the list
            if($t%3 == 0 || $t == count($terms)) { ?></ul><?php
            // if "t" is a multiple of 6, or the very last item, close the row
            if($t%6 == 0 || $t == count($terms)) { ?></div><!-- end row --><?php
        }
    endforeach; ?>
</div>