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 Palau.
It is prohibited to sell or serve any alcohol beverage to a person under 21 years of age. Minors may access a bar or licensed premises only if accompanied by a parent or legal guardian. Minors buying, consuming or attempting to buy alcohol are committing an offence. The law provides an exception for the consumption of alcohol by minors as part of a religiously recognized ceremony.
You can find more legal details and links here:
Wikipedia Legal Drinking Page