How to make my iTunes account zero balance?

Either enter in a credit or debit card temporarily and buy something more expensive than your remaining balance, or contact iTunes Support and ask them to clear your balance for you.

iTunes - Official Apple Support

Regards.

I see you want to empty your account balance. This is not something the people on this forum—other users like yourself—can do for you. You can use one of the methods below:

1) If you are trying to zero your balance and still have a valid credit or debit card from your original country, you may purchase an item from the App or iTunes Stores for more than your balance. The remainder will be billed to your card, leaving you with nothing in your account balance. This is the easiest solution (you can do it yourself!), plus you get to use your money for something for yourself instead of donating it to Apple.

2) Alternatively, you could ask Apple Support to remove and keep the balance. Use this link Apple provides to take you directly to the managing and editing an Apple Account people who will do this for you --> https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0998&symptom_id=20198

This is more direct than using Official Apple Support which will just eventually lead you to the same place after some searching.

If the above direct link does not work for you, go to https://getsupport.apple.com/?s=n , enter “empty balance” or “zero balance” in the search line, press enter to search, then on the next page select “Clear Apple Account balance”. On the next page select a chat or telephone call option.

Alternatively give Apple a phone call. Find a list of telephone numbers at: Contact Apple for support and service - Apple Support

When asking about this because you are changing regions, take a look at this article:

Change your Apple Account country or region - Apple Support