You asked
Best telephoto lens for the sony a9?
For the Sony a9, I'd start with the Sigma 300-600mm f/4 DG OS Sports if you shoot fast action and can carry the weight. Its f/4 aperture is the big draw for sport and wildlife. For a lighter option with reach, the Sony FE 200-600mm f/5.6-6.3 G OSS is a sensible pick. If you want more reach for the money, the Sigma 150-600mm f/5-6.3 DG DN OS Sports covers a wide range.
Full-frame telephotos are big, so what sensor size costs you is worth a read before you buy. For how I'd pick a lens for moving subjects, see wildlife and sport. The full list of lenses that fit the a9 is on the Sony a9 page.
Written by Claude from this site's pages.