Yes, it is set to public and I will research further into Custom Roles and post what I discover. Please do the same.
function cpt_team_posts() {
$labels = array(
'name' => _x( 'Team Posts', 'Post Type General Name', 'site_intranet' ),
'singular_name' => _x( 'Team Post', 'Post Type Singular Name', 'site_intranet' ),
'menu_name' => __( 'Team Posts', 'site_intranet' ),
'name_admin_bar' => __( 'Team Post', 'site_intranet' ),
'archives' => __( 'Item Archives', 'site_intranet' ),
'attributes' => __( 'Item Attributes', 'site_intranet' ),
'parent_item_colon' => __( 'Parent Team Post:', 'site_intranet' ),
'all_items' => __( 'All Team Posts', 'site_intranet' ),
'add_new_item' => __( 'Add New Team Post', 'site_intranet' ),
'add_new' => __( 'Add New', 'site_intranet' ),
'new_item' => __( 'New Team Post', 'site_intranet' ),
'edit_item' => __( 'Edit Team Post', 'site_intranet' ),
'update_item' => __( 'Update Team Post', 'site_intranet' ),
'view_item' => __( 'View Team Post', 'site_intranet' ),
'view_items' => __( 'View Team Posts', 'site_intranet' ),
'search_items' => __( 'Search Team Post', 'site_intranet' ),
'not_found' => __( 'Not found', 'site_intranet' ),
'not_found_in_trash' => __( 'Not found in Trash', 'site_intranet' ),
'featured_image' => __( 'Featured Image', 'site_intranet' ),
'set_featured_image' => __( 'Set featured image', 'site_intranet' ),
'remove_featured_image' => __( 'Remove featured image', 'site_intranet' ),
'use_featured_image' => __( 'Use as featured image', 'site_intranet' ),
'insert_into_item' => __( 'Insert into team post', 'site_intranet' ),
'uploaded_to_this_item' => __( 'Uploaded to this team post', 'site_intranet' ),
'items_list' => __( 'Team post list', 'site_intranet' ),
'items_list_navigation' => __( 'Team post list navigation', 'site_intranet' ),
'filter_items_list' => __( 'Filter Team posts list', 'site_intranet' ),
);
$args = array(
'label' => __( 'Team Post', 'site_intranet' ),
'description' => __( 'Intranet Team Posts', 'site_intranet' ),
'labels' => $labels,
'show_in_rest' => true,
'supports' => array( 'title', 'editor', 'comments'),
'taxonomies' => array( 'team-post-sections' ),
'hierarchical' => false,
'public' => true,
'show_ui' => true,
'query_var' => true,
'show_in_menu' => true,
'menu_position' => 5,
'show_in_admin_bar' => true,
'show_in_nav_menus' => true,
'can_export' => true,
'has_archive' => true,
'rewrite' => array (
'with_front' => false,
'slug' => 'team-posts'
),
'exclude_from_search' => false,
'publicly_queryable' => true,
'capability_type' => array('team-post','team-posts'),
'map_meta_cap' => true,
);
register_post_type( 'team-posts', $args );
}