Cut near the ground, then take a dauber full of roundup/glyphosate concentrate and carefully put it on the cut, making sure to coat the outer edge of the cut.
You want to make sure to get it on the cambium layer in the bark, as this will be where the privet pulls the roundup down into the root, killing the extensive root system that privet can develop.
Note that even with using roundup it may take a couple years to actually kill the privet.
Cut near the ground, then take a dauber full of roundup/glyphosate concentrate and carefully put it on the cut, making sure to coat the outer edge of the cut.
You want to make sure to get it on the cambium layer in the bark, as this will be where the privet pulls the roundup down into the root, killing the extensive root system that privet can develop.
Note that even with using roundup it may take a couple years to actually kill the privet.