For HP ink cartridge customer service, you can contact HP experts for support with printing and ink-related issues through phone or live chat.

Here are the direct options:
– **Home Customers Sales & Support:** Call 888-999-4747, available 7 days a week from 9 am to midnight EST.
– **Live Chat Support:** Available 7 days a week, 9 am to midnight EST for home customers[1].

If you specifically need assistance with HP Instant Ink subscription or replacement service, HP offers support via their Instant Ink support website and customer support telephone. You can manage your subscription, get help with ink delivery, or solve cartridge issues through these services[2][3][5].

Note that HP Instant Ink cartridges only work when your subscription is active, and you can also use original or refilled HP cartridges with the proper chip, but details vary depending on your printer model and subscription status[3][5].

If you want to update your mailing address or other account details related to ink cartridges and subscription deliveries, you should do so via your HP Instant Ink dashboard or by contacting HP customer support[5].

In summary, the best way to get help for HP ink cartridges is to call the HP customer service number for home customers at 888-999-4747 or use their live chat during supported hours. For Instant Ink specific issues, use the dedicated HP Instant Ink support channels[1][2][3].