It depends on the app.
If the app developer chose to save progress in the backed up portion of ther app directory, the the points will come back when you restore the old iPad's backup to the new one. Be sure to do a backup before switching.
If the app stores it's game progress in a cloud account (iCloud, google drive, whatever) then the points will be restored when you sign into the new account in the app. If the app does not have an account, it probsbably does not use this method. Not unless it uses iCloud.
If the app keeps all it's data on the iPad, and does neither rof the above two, then there is no way to keep your points.
You can try going to the app's developer website, if they have one, and asking. Otherwise you can hope the app is popular enough to have a some social network presence and ask that community for their experiences.
Note. There is a small chance that Game Center on the iPad keeps score info that will be automatically restored.. I don't know if this is true, but having Game Center enabled is worth a try.