"Level Six, Department of Magical Transportation, incorporating the Floo Network Authority, Broom Regulatory Control, Portkey Office and Apparation Test Centre."
-- voice in the Ministry of Magic lift (OP7)
Broom Regulatory Control is part of the Department of Magical Transport (OP7), but it is not clear what functions they perform. Since underage students are permitted to fly on broomsticks without any formal licensing process, licences do not appear to be a requirement for broomstick use.
It is possible, though only a speculation, that Broom Regulatory Control concerns itself with whether broomsticks meet adequate safety standards rather than whether the users meet a specified level of competence - e.g., whether broomsticks have adequate Braking Charms, for example, or whether the Flying Charm on a broomstick is up to standard.