Is it possible to have a star orbiting around a brown dwarf?
Yes

If a brown dwarf count as a star in this case, the solution is as easy as a smaller brown dwarf orbiting a larger one.

If not, it is still possible if you have two brown dwarfs orbiting close to each other, both just too small to be red dwarfs, together out-massing an orbiting red dwarf, just large enough to be counted as a star.

While I have no example of such a system, the Alpha Centauri system has to closely orbiting stars, with a more distant star orbiting, and Luhman 16 is a system with two brown dwarfs orbiting each other.