the reaper appears randomly, but it only appears when you kill something, mainly sheep, cows, pigs, spiders, zombies, pretty much any mob that would normally be kindof weak stat wise. if you have the right amount of armour, weapons, etc, then you can kill one pretty easily. Watch out though as you never know when you kill something and they'll pop up, just make sure that you hunt and kill things sparingly or else they will pop up more.There is also a chance that it will spawn during "Shadow Games" where mobs randomly spawn and day is quickly turned to night
Also they're called 'Reapers' for a reason, by killing something you're pretty much asking to be killed yourself by the Reaper