Change description on specific WooCommerce product status change

To avoid an infinite loop on transition_post_status hook when using wp_update_post(), try:

add_action('transition_post_status', 'new_product_add', 10, 3);
function new_product_add($new_status, $old_status, $post) {
    if( 
        $old_status != 'publish' 
        && $new_status == 'pending' 
        && !empty($post->ID) 
        && $post->post_type === 'product'
    ) {
        $term = get_term_by('name', 'فروش پیج اینستاگرام', 'product_cat');
        wp_set_object_terms($post->ID, $term->term_id, 'product_cat', true);

        // unhook this function so it doesn't loop infinitely
        remove_action( 'transition_post_status', 'new_product_add', 10 );

        wp_update_post( array('ID' => $post->ID, 'post_content' => "something"));

        // re-hook this function
        add_action( 'transition_post_status', 'new_product_add', 10, 3 );
    }
}

Or:

add_action('transition_post_status', 'new_product_add', 10, 3);
function new_product_add($new_status, $old_status, $post) {
    if( 
        $old_status != 'publish' 
        && $new_status == 'pending' 
        && !empty($post->ID) 
        && $post->post_type === 'product'
    ) {
        $term = get_term_by('name', 'فروش پیج اینستاگرام', 'product_cat');
        wp_set_object_terms($post->ID, $term->term_id, 'product_cat', true);

        $product = wc_get_product($post->ID);

        // unhook this function so it doesn't loop infinitely
        remove_action( 'transition_post_status', 'new_product_add', 10 );

        $product->set_description("something");
        $product->save();

        // re-hook this function
        add_action( 'transition_post_status', 'new_product_add', 10, 3 );
    }
}

It may solve your issue.

This is documented here on wp_update_post() for save_post hook.