When people ask me this, I always return with... 3 Questions:
-> What's your budget?
-> What do you intend to photograph?
-> Do you know how to get close or do you like to stay far?
Without knowing one and two, it's hard to assemble a kit. Without knowing 3, helping you with a lens is a crap shoot.
Here's the honest truth... for about 50 years, a 500mm lens was considered an extreme telephoto focal length. A ton of wildlife photography was done with 400mm, and my first successful attempts with wildlife was with 300mm. These days, people like to stay in their car, shoot from the road, grab a shot, and crop the crap out of it (see what I did there
). There's nothing wrong with the latter, but it mostly results in "got it shots" that are just good enough for Insta and Facebook.
If you are willing to invest in your technique and accept that you will miss some shots of distant animals, I can suggest a kit that would be about $3300 out the door.
The Nikon Zf with 24MP sensor, though designed for more street-like photography, has a super capable AF and will allow for a high in-focus rate at 10fps. It costs $2000 new.
The Tamron 100-500 Z-mount is a very high quality lens and will out perform your 200-500... it is $1200 or so.
Probably the best budget kit in the Nikon ecosystem.
bruce