When you set up a new Stripe account and configure it in Chargebee, all the new signups will directly go to this new account. For this, you'll have to set the new Stripe account under Smart Routing (Settings >> Payment Gateways (under Billing) >> Manage Rule (on the right)).
However, your existing customers' payment information would still be stored in your old Stripe account. So, they need to be moved to the new Stripe account and then remapped with the respective customer accounts in Chargebee for the payments to go through successfully.
If there are only a few customers, you could use our "Request payment method" option to send an email to your customers and ask them to re-enter their payment information.
However, if you do not want to request the customers to update their payment information again, just log into your Chargebee site and navigate to Settings >> Import & export data >> Raise a migration request and raise a request. Based on the information, you provide here we will guide you on how to proceed.