How can I get a paginated list of custom taxonomy tags with posts?

This code was not tested!

Tested

Based on @Pieter Goosen answer
.

<?php
$post_type="item";
$taxonomy = 'item_tags';

// count the number of terms for correct pagination
$term_count = get_terms( array (
    'taxonomy' => $taxonomy,
    'fields'   => 'count',
) );

// define the number of terms per page
$terms_per_page = 10;

// find out the number of pages to use in pagination
$max_num_pages = ceil( $term_count / $terms_per_page );

// get the page number from URL query
$current_page = get_query_var( 'paged', 1 );

// calculate the offset, if there is one.
$offset = 0; // initial
// or changed the if not the first (0)
if( ! 0 == $current_page) {
    $offset = ( $terms_per_page * $current_page ) - $terms_per_page;
}

// get all taxonomy terms
$terms = get_terms( array (
    'taxonomy' => $taxonomy,
    'order'    => 'ASC',
    'orderby'  => 'name',
    'number'   => $terms_per_page,
    'offset'   => $offset,
) );

echo '<dl>';

// cycle through taxonomy terms
foreach ( $terms as $term ) {

    echo '<dt>' . $term->description . '</dt>';
    echo '<dd>'; 
    echo '<ul>'; // because you can't have multiple <dd>s for one <dt>

    // cycle through posts having this term
    $items = get_posts( array (
        'post_type'   => $post_type,
        'tax_query'   => array(
            array(
                'taxonomy' => $taxonomy,
                'terms'    => $term->term_id,
            ),
        ),
        'numberposts' => -1, // different from WP_Query (see Code Ref)
    ) );

    // essential, see comments inside foreach() loop
    global $post;

    foreach ( $items as $item ) {

        // assign $item to global $post 
        $post = $item;
        // and now set up 
        setup_postdata( $post );

        echo '<li><a href="' . get_the_permalink() . '">' . get_the_title() . '</a></li>';
        // wp_reset_postdata(); // see below
    }
    wp_reset_postdata(); // moved outside the foreach() loop

    // end posts cycle
    echo '</ul>';
    echo '</dd>';
}
// end term cycle
echo '</dl>';

// Pagination
// See the Code Reference for more arguments
echo paginate_links( array (
    'total'   => $max_num_pages,
    'current' => $current_page,
) );