Out of the box, no. Inside of the Admin UI you can go and update the payment information for an order, but that is only for store admins, not the customer. You could build a Payment Form page and have the user go there to update the payment info. You will need to figure out how to redirect the user once they have updated their payment, but it shouldn't be too tough. Just look adding your code in the ProcessData method of the form.
https://docs.kentico.com/display/K82/Creating+a+custom+payment+gateway#Creatingacustompaymentgateway-Creatingacustompaymentgatewayform