As your level increases, the number of beasties that can roam your kingdom increases also.

Go to some unused corner of your kingdom, use a beastie potion. Repeat until you have the maximum number of beasties allowed at your level. Then just leave them there. They may be blocking a wall or rock or something unimportant, so it doesn't matter. You can then build a 'pen' around them, but you really don't need to. It just looks cool to have them in a pen.

I like to have one of each 'penned' in my kingdom, in case I get a quest that calls for banishing a certain kind or I need something specific from a beastie (fur, ears, tails, etc.)

Thank you very much

Yes there is. You can only have 3 beasties at any time on your property. with potions bought with hearts you can set up a pen somewhere you choose to leave 3 of them to mill about. no more pop up beasties.