How do I make a new payment method the default one?

Note that your personal account balance will always be your default method unless the item cannot be paid that way.

From this support article --> How apps, content, and subscriptions from Apple are billed - Apple Support

"Which payment method is charged?

When you buy items or pay for subscriptions, Apple automatically attempts to charge your payment methods in this order:

1. Apple attempts to use your Apple ID balance to cover the full amount.

2. If you don't have Apple ID balance, you don't have enough to cover the full amount, or an item cannot be paid for with Apple ID balance, Apple attempts to charge your primary payment method (typically a credit or debit card, but varies according to country). The primary payment method is at the top of the list in Settings on your iPhone. You can control which payment method is at the top of the list. [See: Add a payment method to your Apple ID - Apple Support ]

3. If there's a problem with the primary payment method, or if the primary payment method can't be charged for the full remaining amount, Apple attempts to charge your other payment methods in order from top to bottom. If none of them can be charged, Apple may try again."

On an iPhone, open the Settings app, tap your name, tap Media & Purchases, tap View Account, tap Manage Payments, tap Edit at the top right of the screen and then move the payment you want to be the default to the top of the list.