Increment paged on WP_Query

You need to create a new WP_Query instance with the updated arguments. I will usually write it like this

$args = [
    'post_type' => 'employee',
    'post_status' => 'any',
    'posts_per_page' => 10,
    'paged' => 1,
];
$query = new WP_Query($args);

while ($query->have_posts()) {
    // your logic goes here
    // foreach ($query->posts as $custom_stuff) {}

    // prepare for next loop iteration
    $args['paged']++;
    $query = new WP_Query($args);
}

When the first run is done, $args['paged'] is updated and the $query variable is updated with a new WP_Query instance. if $query->have_posts() is true, the loop will then continue.