You can update your credit card from https://yourcommunity.mobilize.io/main/settings/billing (or https://community.yourbrand.com/main/settings/billing if you're using a Custom Domain). Navigate there via your Community Settings. You'll need to be the Account Owner in order to access billing. Community Managers do not see the Billing tab at all.
Click the Community Menu icon in the upper right, choose Community Settings, and go to Billing. You don't need to update your plan. There's a light gray link to update your credit card. It says Change payment method. Here's what it looks like in a test account.
After changing the credit card, the system will automatically retry the card within 3-7 business days based on an automatic schedule. It won't retry the card immediately. If you need the charge to go through sooner, please send a quick chat via the platform or email us at firstname.lastname@example.org.