Proper translation for the exotic pets exotic pet is translated on iciba as 


  外来宠物


VICE also translated it the same way in a video of theirs, also adding


  外来物种


And my absolute favorite


  野生猛宠


is there a common well known term for exotic pets? 野生宠物？
the SPCA hong kong used "珍奇品種寵物" for exotic pet.

http://www.spca.org.hk/ch/animal-welfare/welfare-law-development/exotic-pet-laws

click the flag to toggle between traditional chinese &amp; english :)

imo, turtles, or parrots are not fierce. so, 野生猛寵, the "猛" is, not descriptive for certain species of exotic pet