In Hogwarts, there are a few sections that are restricted to some students. Here are the ones that are restricted and reasons why and the age at which they can be accessed.
Hogwarts Library Restricted Section
The Restricted Section is an area in the Hogwarts Library closed off by a rope and only accessible to students with permission from a professor; in order to enter, they must present a signed note from a professor.
Some of the books in the library are chained to the shelves, which would suggest some of them are particularily valuable. The books within the Restricted Section typically discuss the Dark Arts or other information not for the general public or young children.
This section of the library is mostly visited by students from 3rd Year, 4th Year, 5th Year, 6th Year and 7th Year.
Chamber of Secrets
The Chamber of Secrets is just what the name says. It's a secret chamber that has been created by Salazar Slytherin when he was still alive. It housed an Ancient Basilisk that was killed by Harry Potter in 1992.
The only people that may enter the chamber are ones who can speak the Serpent tongue. The only Parstletongue currently alive is Harry Potter however it may be possible that one of his children has this gift as well.
Room of Requirements
This room can be accessed by anyone if they know how to access it and where this particular room is. Most of the time only the fifth, sixth and seven years are ones who are more or less successful in accessing this room however there is a spoken rule that none of the people who know how to access this room will tell anyone.