Switch from basic support to enterprise support

All you need to do is open a support case under Account and Billing category from Org account(payer account) mentioning the account details of the child account that is still on basic support plan.

Remember logging the case from payer account not from the child account which has basic support plan.

Mentions something like below in your support case logged from payer account:

"The account(Child Account Name, Account Id that has basic support plan) has been merged with with payer account <Account id and Account Name>. Request a support plan change of this account from current Basic support plan to Enterprise support plan."

Hope this helps.

Comment here if you have additional questions, happy to assist.

Abhishek