Read this support article about updating the birth date for a child Apple Account to a non-child status: Update the birthday associated with an Apple Account - Apple Support
“To change a birth date of any child account set to an age below 13*, you might have to wait for the account to naturally age up. If you see ‘your birth date cannot be changed to this date’, you can’t change to a birth date that would no longer be a child account.”
Without actually trying to change ages on an account myself to test what is possible, the second sentence suggests to me it may be possible to change to a younger age but not to an older one.
Apple says, “Might have to wait.” Earlier versions of the article said, "If you need to change the birth date for someone below age 13, contact Apple Support,” but that was removed from the support article late 2024. Apple’s wording in its support articles is sometimes open to interpretation and they dislike using definite terms, particularly if it has a negative context. Since “might” also leaves open the possibility ”might not”, I wonder if contacting Apple and asking them to do this is still an option? This page has telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support
An alternative would be to create a new Apple Account (losing some things done with the previous one) . If this is going from a younger child to an older child, but still a child according to Apple, use this method ➔ Create an Apple Account for your child - Apple Support If this is for a child to an adult aged account, use this method ➔ How to create a new Apple Account - Apple Support