What would happen if we stopped discovering new things?

The rate of change of society wouldn't slow for a long time as we are nowhere near fully exploring everything we can do with current technology, and rolling that technology out to all potential locations and uses.

Further, the technologies that enable us to make discoveries have themselves not been fully explored, so it would in fact be difficult for discovery to stop. As an example, we have the technology to sequence genomes. Each successive genome that we sequence could be argued to be a discovery in its own right, and each facilitates new discovery (e.g. finding novel useful genes).