@Macker-99
I am not aware of any printers that require Instant Ink service.
The print-by-page subscription Instant Ink service is not mandatory.
Instant Ready Cartridges that may come with your printer are just that - Instant Ink Ready
You need not subscribe to Instant Ink.
You need not remove the cartridges.
When you set up the new printer, simply decline any offers to subscribe to the service.
Use the ink that comes with the printer and when it is time, install a new set of purchased HP Ink cartridges.
Reference and Resources – Places to find (more) help and learn about your Device
Clarification of terms and "what the device can do" (Specifications)
Device Homepage
NOTE: Content depends on device type and Operating System
HP Drivers / Software and BIOS, How-to Videos, Bulletins/Notices, How-to Documents, Troubleshooting, Manuals, Product Information, more
Open Support Home
Enter the name of your device
When the website support page opens, Select (as available) a Category > Topic > Subtopic
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Dragon-Fur