You asked
Best telephoto lens for the nikon d7200?
For the D7200, I'd start with the Nikon AF-S 70-200mm f/2.8E FL ED VR. It frames like 105-300mm on this body, it's fast enough for indoor sport, and it's a solid all-rounder.
If you need more reach for wildlife, look at the Nikon AF-S 200-500mm f/5.6E ED VR, which frames like 300-750mm, or the Sigma 60-600mm f/4.5-6.3 DG OS HSM Sports, which frames like 90-900mm. The D7200 has no stabilisation in the body, so stick with lenses that have VR or OS, as all of these do.
If you shoot fast action in low light and can carry the weight, the Sigma 120-300mm f/2.8 DG OS HSM Sports is the one I'd pick. It frames like 180-450mm and is very capable.
For how focal length translates to your subjects, see wildlife and sport.
Written by Claude from this site's pages.