That's no problem, simply log on to your account with your chosen plan provider to update your card details.
You can add multiple payment methods to your Partial.ly customer account. To add a new payment method, login to your Partial.ly customer account, select the payment methods section and select the 'add a new payment method' button.
Below are some useful links for you:
All Countries - Partial.ly - https://partial.ly/login
US Zip (formerly Quadpay) - https://customer.us.zip.co/en-US/login