Assuming you’re on phone.
You just download the APK of the new version and install it as an update.
It may fail, it’s often because Android likes having a lot of free space.
Other option is to backup your saves, uninstall and install the game again so you can put the saves back there manually.
WHERE ARE SAVES LOCATED ON ANDROID? Android/data/com.domain.corruptedkingdoms/files/saves
NOTE: If you’re running Android 11+ then Google has hidden your data folder. To access it you need to connect your phone to your PC with a USB cable or use an app like Solid Explorer or X-Plore to give you access to the folder again.