Hey ilene118,
A new cable box should not impact your ability to download or access the Apple TV+ app from the Smart Hub on your Samsung TV, but you may need to sign in again from your mobile device.
These are the instructions we found on the Samsung website.
How do I sign into the Apple TV app on a Samsung TV or projector?
Before you can sign into the Apple TV app, you must have an Apple Music or iTunes account. If you have never used Apple Music or iTunes, you need to set up an account in the Apple Music app on your phone or iTunes on your PC.
1. Navigate to and select the Apple TV app.
2. Select Settings, and then select Accounts. Select Sign In, and then select Sign In On Mobile Device.
3. Two sign-in options are available. Using your phone, either navigate to the Apple TV activation page and enter the code that is displayed on your screen, or scan the QR code that appears.
4. Use the on-screen instructions to complete the sign-in process.
5. Note: For more information or if you need help signing in, visit Apple Support.
How to use the Apple TV App on your Samsung Smart TV
If you're still unable to sign in, try to delete and reinstall the Apple TV+ app. We found these instructions on the Samsung Care YouTube channel.
How to delete Apps from Smart Hub on your TV
Install Apps from Smart Hub on your TV
Kindest Regards.