We get a lot of questions about Instant Ink, the most common question being how it affects using "normal" or cheaper compatible cartridges that are not part of Instant Ink.
NO, you can not use compatible cartridges when signed up to Instant Ink.
Instant Ink is designed to tie users into using original ink HP ink. If you were to replace an HP cartridge with a lower priced compatible your printer would reject those cartridges.
Furthermore, if you were to cancel your HP Instant Ink agreement the cartridges still in your printer will no longer function and you would need to buy replacements.
HP Instant Ink is about making a commitment to use their HP branded ink. If you'd rather have the freedom to choose which cartridges you use, potentially saving money in the process, then HP Instant Ink may not be for you.
Read more about HP Instant Ink here.