We have a Family Link. How can I buy the Premium version for my child?
Family Link is a Google tool, which allows to create a family group for parents and children. When administrator setup children’s device settings, he/she can add a common payment method, which will be used by purchase apps from child’s device.
A family group administrator can turn on the purchase approval feature. With using that, the child must obtain administrator approval before each purchase.
Please note that the Premium version is connected to a gmail account, from which purchase was done. If you bought the Premium version on your child’s device with his/here own gmail account, then Premium will not be available on your device with your(different) gmail account.
The family group administrator can manage the shared payment method and track member purchases.
How to setup payment options:
Open Google Play
At the top right, tap the profile icon.
Tap Payments & subscriptions > Payment methods.
If you don’t already have a credit or debit card added as a payment method, tap Add credit or debit card.
Follow the instructions to add a new payment method.
Under “More options,” tap Change family payment method.
Select a new payment method.
You can read more details by this link in Google Play support.