To change your payment method or payment details, you have to cancel your current subscription in the billing tab of your account settings and then set up a new one with your new payment details by buying the needed premium membership on the Upgrade page. You can do it right now or just before the membership expires:
If you do not see the Cancel Subscription button, you can skip the aforementioned cancellation process and proceed with the purchase.
And you do not have to worry about the remaining days of your current premium membership going to waste as they will be accounted for as discount for your new purchase as shown below:
To change your billing information, please refer to this article.