The Animal Empathy adept power lead me to the question which skill is enhanced through it? I personally could imagine both Leadership and/or Instruction but I'm just not sure about it.
Other opinions / an official call I missed?

There have been references to Paranormal animal handlers and trainers for the last several editions, to my knowledge there has never been an actual skill to use.

The mechanics I used in SR3 were to create an Animal Training skill with specializations per critter. Base time for training a given trick was 1 month divided by successes. I set the threshold fairly ad hoc depending on the difficulty of the trick and relationship to the animal's instinctive response.

Teaching a hellhound to breathe fire on command is simpler than teaching it to play dead for example.

I did roughly the same and had the player create a new skill called: Animal Handling. If he wanted to breed the animals then he also needed: Animal Husbandry. He would roll his Animal Handling skill anytime he wanted the critter to do something that was against it's nature, even if it was trained.