The Beast Link spell has a cast time for an action. Then it lasts 10 minutes (or until its concentration is broken).
It can only be used on a beast that is already friendly to you or enchanted, so it practically limits it to the companion of a Beast Ranger or requires you to first protect an animal.
After the spell ends, the beast remains just an animal that is likely to be friendly or enchanted (unless the spell has broken). He will behave according to his nature: a wild animal will probably leave when he can.