Yes, if you change the root URL of your blog, HubSpot will automatically set up redirects for you.
For example, if the blog was located at example.com/blog, and then the root URL was changed to example.com/hubspot, we would automatically redirect www.example.com/blog/mypost to www.example.com/hubspot/mypost.
If you've imported blog posts and the original root URL of the posts is different than the one set within HubSpot, you will see a message confirming that you'd like to update the URL of the posts from the original root directory (e.g. /blog/) to match the blog's new root directory (e.g. /new-blog/).