There is no account system in Grid Diary Classic, all your data is stored locally on your device. So you need to transfer the data to Grid Diary 2 manually.
Method A (Recommended)
Please upgrade to Grid Diary Classic (4.2.6+), Grid Diary 2 (1.0.4).
Open Grid Diary Classic (4.2.6+), Tap home button, tap the "..." button, and then go to "Settings"
Go to "Data" - "Advanced" - "Export JSON". And then wait for exporting
Choose "Open In Grid Diary 2" in the popup window
In Grid Diary 2, tap “Import” and wait for the process to complete
Please update to Grid Diary Classic (4.2.4+), Grid Diary 2 (1.0.4).
Open Grid Diary Classic
Switch to Grid Diary 2. Tap "Me" - "Data" - "Backup" - "Import Grid Dairy Classic Data" - "Open Grid Diary Classic"
Wait until complete. It might take a few minutes if you have a lots of data in the Classic version
If you have Grid Diary Transfer File (GDJSON) saved in Files.app or other places, you can directly import it to Grid Diary 2 as well.
In Grid Diary 2, tap "Me" - "Data" - "Backup" - "Import Grid Diary Classic Data" - "Browse GDJSON File"
After successfully transferring your data and subscribing to the new Grid Diary, you can delete Grid Diary Classic to free up space.