Can a fan page make money on Instagram?

Yes you can create a fan page and monetize it. However, the posts you use will be created by other people as it is unlikely you will be in a position to follow the famous person around every day and take photos. To use posts you do not own you must give credit to the owner and usually make a statement in your Bio that states “photos belong to respective owners”. If you do not give credit you risk having your page disabled or deleted by Instagram. There is an excellent fan page account for Angelina Jolie on the Buy Shoutouts site with over 5 Million followers. They get $200 an hour for paid promotions.