I have an old version of WebStorm, and I do have a license for it. How do I upgrade my WebStorm version to the newest one and transfer my license to the newer installation?
Just download a new version from https://www.jetbrains.com/webstorm/download and register it with your license (using your JetBrains account or with offline code). See https://www.jetbrains.com/help/webstorm/registering-webstorm.html
Should you have problems registering it, please contact support