This is Ontario specific, but you cannot install a receptacle in a closet unless it has a single specific use case. This is proven during the ESA inspection when you would tell them it's only there to provide power to the closet lighting.

If the floor is out, a decent method is to extend an existing receptacle, drop the romex down to the floor plate (just above it), still running it through holes drilled in the vertical studs. If your trim is tall enough, you don't even have to patch anything.

Just run it to the spot you want, put in a rework box, and you are done without having to do any drywall work. Fish the romex through the holes you drill in the stud bay, add nail plates, and do all the work through the hole you cut for the new box.

You could also add a receptacle on the outside of the closet also, directly across from the one you want to add inside the closet. You are in there already and nobody has ever complained about too many receptacles.