How do you get clippers in Rune Factory Frontier?

Answer 1

You get them from Egan.

Check the Help Board until you see the request "Please Taste This for Me". Answer his little questions and he'll give you the Clippers if you complete the request.

Answer 2

There aren't any clippers in RFF; if you need to get wool from a beast like a Wooly you need to get a Harvester from Candy. With the Harvester you can do many things like get milk or wool.