Yes. An operator must provide a notice to the parent, and a notice on the website.
Direct notice to the parent. An operator must make reasonable efforts, taking into account available technology, to ensure that a parent of a child receives direct notice of the operator's practices with regard to the collection, use, or disclosure of personal information from children, including notice of any material change in the collection, use, or disclosure practices to which the parent has previously consented.
Notice on the Web site or online service. In addition to the direct notice to the parent, an operator must post a prominent and clearly labeled link to an online notice of its information practices with regard to children on the home or landing page or screen of its Web site or online service, and, at each area of the Web site or online service where personal information is collected from children. The link must be in close proximity to the requests for information in each such area. An operator of a general audience Web site or online service that has a separate children's area must post a link to a notice of its information practices with regard to children on the home or landing page or screen of the children's area. To be complete, the online notice of the Web site or online service's information practices and must state specific information as required by 312.4
Reference: 16 CFR 312.4 Notice