If the answer above is None it means there is no specific mention in the legislation, but you still need to ask local law enforcement before drinking in Turks and Caicos Islands.
It is prohibited to serve or sell liquor to a young person under the age of eighteen years. Minors under the age of sixteen years may not present in a licensed premises mainly serving and selling alcohol beverages.
You can find more legal details and links here:
Wikipedia Legal Drinking Page