permalink and URL issue

Installed wordpress into a subfolder on a server which hosts several of my clients’ websites. The site works fine but the url that displays in the browser reflects the path that I installed wordpress on (https://hostingserver.com/client-sub-folder) rather than the clients URL (https://client-url.com). I’ve been looking through the codex but am not sure if any of the articles I’ve found pertain to my specific situation.

From What I’ve found it looks like I could get the desired result by simply changing the “Site URL” in the general settings area of the admin, but what implications will this have on the site and the permalinks? Will the image and post links be broken or need to be changed?