Loyalty doesn't have to mean a creature will always stick around. Creatures may have an instinctive drive to mate, raise young, migrate, etc. It might be loyal to you but want to live its own life when it matures or comes into its own.
Bonds of loyalty could also be the result of the PC helping or saving the creature (e.g. it's caught in a trap; was born malformed, been abandoned by its pack, and can't survive on its own; or been wounded in a fight with another creature or its own kind). In such cases you can cap the creature's stats or abilities (hits, OB, DB, movement, etc.) to reflect its permanent injury, which will help mitigate any unbalancing affects a "normal" creature might introduce.
If you're introducing this as a young creature, perhaps it's the runt of the litter and the PC must act as surrogate parent to form the bond. This particular creature will never grow to become as powerful as a normal creature of its kind (50% as powerful? 75%? it's up to you), which could make for a good story that again tempers any unbalancing affects of allowing a "normal" unusual creature.
"Hey, your one-winged baby gryphon is cute as a button! What's wrong with its eye?"