To change the card where the subscription is charged, you'll just need to add the new card and update the Funding Source in your Paypal account.
Here's how to do it (there might be a discrepancy with the screenshots as Paypal is currently running an update on their website design)
Step 1: Login with your Paypal account at https://www.paypal.com/
Step 2: Click on the gear icon on the upper right hand on your screen
(Sometimes, some Paypal accounts would show a different interface, but it's usually just clicking the avatar at the upper right of the screen and clicking Account Settings)
Step 3: Click on Payments (or Money) in the menu, click "Link a new card" - enter your new card details and this would save the card to your Paypal account.
Step 4: After linking the new card, click on Manage Pre-approved Payments
Step 5: Click on "Set Available Funding Sources"