How to change parent permalink?

I have a theme with hardcoded permalink structure for some posts. Those posts open with

site.com/parent/page

structure.

I created a filter that replaces the link from "site.com/parent/page" to "site.com/newparent/page" in functions.php with:

add_action('init', 'change_slug_of_post_type_parent', 20);
function change_slug_of_post_type_parent()
{   
$args = get_post_type_object("parent");
$args-rewrite["slug"] = "newparent";
register_post_type($args-name, $args);
}

Links are now generated OK, but when I click on them, the page doesn't load.

Can someone please help? I am sure this is easy fix, but I cant get around it. I am new to wordpress programming (I used GSCMS, and CMSGS before).

Thanks