Wildlife portraits are just like any other portraits, so lighting and making the eyes grab our attention are just as important as they are in pictures of people. Poses are also vital, although with wildlife we are lucky if they respond to direction. We did come across a snowy owl once that obligingly moved from in front of a white wall to a better background, but perhaps it was hoping for success in movies or something. As regards lenses, a standard zoom is good for captive creatures who are up close, so on APS-C that would be my 18-135mm. For further away, then the 55-300mm comes into its own. For portraits we do need to be reasonably close, so longer lenses don't get used for this as often, but we have a 150-450mm for when it's needed.
Over the shoulder pose from this Pheasant
Shellduck in profile
The eyes have it
Little Owl in a studio setting
Eye contact!
The dynamic pose
Crested Southern Screamer
Pretty Flamingo
So Happy Together
Robin on Tyre
Sharp!
Macaw