Hiya Friesy
Is it a back pedal coaster brake? Or a drum brake with a cable and brake lever?
The simplest solution to have brakes in the hub is to fit a Shimano or a Sturmey Archer 3 speed coaster hub. They're tough, easy to find, and not that expensive.
When you start getting further into it there are more options - Shimano also makes internally geared hubs that will take a roller brake - it attaches to the hub gears and is kinda like an external coaster brake. Sturmey Archer make 3 speeds with drum brakes and coaster brakes - the new coaster brake hubs are meant to be really good, the vintage ones are meant to suck. I've used the SA drum hubs & found that up front they're really awesome but in the rear the braking power is pretty mild.
There's a couple of other 3 speed hub makers - SRAM. Fichtel and Sachs who were bought by SRAM and don't exist anymore but can be bought 2nd hand. Hope this helps!