I've been checking the map occasionally and never saw a gryphon there. Is it just coincidence (keep waiting), or do I have to catch some other beasts to make space for gryphs to move in?

Also, if I invite Gryphon Magician, are new gryph(s) guaranteed to appear, or is it just a higher chance?

You need to make space for the new beasts to come. They won't come until they see a free lair.

Gryphon Magician will make all new flying pets to be Gryphons. So to get new Gryphons, you need to clear only other flyers.

Thanks for the answers!