I've been saving Lightroom photos on External hard drive and now its full. What do I do now?

(edited my post because it was an incorrect answer that talked about Lightroom Classic, not the cloud version)

Could you clarify which version of Lightroom you are writing about? You've posted in the "Lightroom ecosystem" forum, which implies you are referring to the cloud-centric Lightroom desktop app, but your description seems more related to the local storage version called Lightroom Classic.

If you are using Lightroom Classic, the answer to your question is yes, you can in fact have your image library stored across multiple hard drives. You could even have some of the drives offline and would still be able to do some functions to the images that are on those offline drives.

But if you are referring to Lightroom Desktop, we will need further details. By default images are stored in the cloud, so local hard drive space would only be an issue if you are using the option to keep a copy of the cloud images on a local drive.