Preheat your smoker. Anywhere between 200 and 250 should be fine (this can go in with whatever else you're smoking). If this is the only thing you're smoking, I'd target 225 °F.
If you're starting with a fat cap that's still attached (like this image), use a knife to remove it from the meat.
Remove any remnants of meat from the fat (because these will burn). Chop the fat into ~½ - 1 inch pieces and place in a baking tin.
Option 1, Long Smoke Method:
Place in the ~225 °F smoker and smoke for 6 to 8 hours until fully rendered. The fat is done when the remaining cracklings are small, golden brown, and most of the liquid in the pan is clear rendered tallow. (I would only do this if other things are going in the smoker; otherwise, follow the short smoke method. You can transfer to the hotter oven at any time to speed up the process, just keep an eye on it)
Option 2, Short Smoke Method:
Place in the ~225 °F smoker and smoke for at least 2 hours.After about 2 hours of smoking, the fat will have taken on plenty of smoke flavor but likely won't be fully rendered.
Transfer to a 325 °F oven and continue cooking until the fat is fully rendered and the cracklings are golden brown, about 1–2 hours. The tallow should be mostly clear and the remaining solids should be small and shrunken.Keep an eye on it during this stage to avoid burning.
Strain and store:
Remove the solids from the pan, then strain through a fine mesh strainer, cheese cloth, or coffee filter into a secondary container.
You can pour the liquid tallow into an ice tray to create 1 tablespoon portions, or pour it into a glass container or mason jar.
Store your finished tallow in an airtight container in the fridge or freezer. It should keep nicely for ~3 months in the fridge or a year in the freezer. Use it in place of oil or butter in your cooking! I love to use it in soups, curries, and stir-fries.