Change custom taxonomy archive permalink

You can use the rewrite parameter to customize the taxonomy permalinks.

Here’s an example which links the taxonomy to the default post post type:

register_taxonomy( 'video_category', 'post', [
    'public'   => true,
    'rewrite'  => [
        'slug' => 'videos/category',
    ],
    // ... your other parameters ..
] );

Don’t forget to flush the rewrite rules — just visit the permalink settings admin page.

And if the taxonomy is being registered by a plugin and (just in case) it doesn’t allow changing the rewrite slug, there’s a filter hook you can use to change the slug programmatically: register_taxonomy_args. Here’s a simplified example:

add_filter( 'register_taxonomy_args', 'my_register_taxonomy_args', 10, 2 );
function my_register_taxonomy_args( $args, $taxonomy ) {
    if ( 'video_category' === $taxonomy ) {
        $args['rewrite'] = (array) $args['rewrite'];
        $args['rewrite']['slug'] = 'videos/category';
    }

    return $args;
}