Can I add my own parental controls to a school-issued tablet?
Usually not, and you should not try. A school tablet is managed by the school, and only one manager can be the device owner. Ask the school what is enforced at home. If you want your own rules, use a separate tablet for home. Skie for Enterprise is the product schools use.
Many schools now give each student a tablet. If it is managed, it already has an owner, the school, and Android allows only one device owner on a device.
That means you cannot add Skie for Parents to the school's tablet. Resetting it to try would break the school's setup and may breach their rules, so please do not. You would also lose access to the school's apps.
What you can do is ask. Find out which apps are allowed, whether the filter works outside school, what the tablet does in the evening, and whether parents get any view of its status. Some schools allow parents read-only status on the tablet, and some leave home use unrestricted. It depends on the school's own setup.
For home, a separate tablet is the usual answer. A low-cost Android tablet set up with Skie lets you choose the apps and hours for reading, play and hobbies, while the school tablet stays the school's.
If your child needs the school tablet for homework, agree the rules at home: where it is used, when it is put away, and charging outside the bedroom.
Schools that want to manage tablets, with a dashboard, groups, timetables and a filter, can look at Skie for Enterprise. This site is about the parents' product.