No, sitemaps do not update automatically in most cases. Sitemaps are essentially lists of a website's pages that are accessible to crawlers or users. They're created by web developers or SEO professionals to inform search engines about the pages on their websites that are available for crawling.
However, there are certain content management systems (CMS) like WordPress that have plugins (e.g., Yoast SEO, Rank Math, Google XML Sitemaps) which can create and automatically update your sitemap when new content gets published. If you're not using such a CMS and plugin, you'll need to manually update your sitemap each time you add new pages to your website.
If you have a large site and need to generate and update your sitemap automatically, consider writing a script that would crawl your website and generate an updated sitemap. Here's a very basic Python example using Beautiful Soup:
Remember to submit your sitemap URL to search engines (using tools like Google Search Console) so they know where to find it. Whenever you update your sitemap, the changes would be picked up during their next crawl.