How to automatically change the category assigned to a post?

Hello,

That code should work fine..
Well, if you need always remove the category “new this week” after 7 days. You can try this code (in your functions.php).

add_action('save_post', 'save_Featured_Removal_options');

function save_Featured_Removal_options($post_id) {
    // check autosave
    if (defined('DOING_AUTOSAVE') && DOING_AUTOSAVE) {
        return $post_id;
    }
		//create scheduled event (7 days)
		$time = time() + 604800;
		wp_schedule_single_event($time, 'clean_my_featured',$post_id);
    }
}

/* hook removal event function */
add_action('clean_my_featured','remove_post_from_featured');

// the function that removes a post form a category and sets a new one
function remove_post_from_featured($post_id) {
    $cat_id = get_cat_ID('new this week');
    wp_set_post_terms( $post_id, $cat_id, 'category');
}

I’m sorry, I hadn’t tried the previous code. Well, here is the new code. I hope it helps.

add_action('publish_post', 'remove_cat_gen');

function remove_cat_gen() {
		global $post;
		wp_schedule_single_event(time()+604800, 'clean_my_post', array($post->ID) );
}

add_action('clean_my_post','remove_cat_from_post');

// the function that removes the category from the post
function remove_cat_from_post($post_id) {
    global $wpdb;
		$cat_id = get_cat_ID('new this week');
		$wpdb->query( $wpdb->prepare("DELETE FROM $wpdb->term_relationships WHERE object_id = $post_id AND term_taxonomy_id = $cat_id" ) );
}