Click your subscription details link to get to "Edit Subscription" menu (If you can't find the link to click, hover your mouse near to the Edit Subscription words until a hand-click icon is shown):
Select "Update Payment Method" and click "Next".
Re-enter your existing or add the new credit card/PayPal account details accordingly. Then click "Update Payment Method".
Here in Orders tab you will see all details of your order:
Switch to Subscriptions to see what payment option you currently have on file. Click "Manage" - > "Update payment method" option:
Update payment method (or if you do not need to change it, just re-enter the billing details anew) and save:
This will trigger an immediate new payment attempt and your Ahrefs subscription will be successfully extended for the next billing period.