You asked
Best telephoto lens for the fujifilm x t4?
For telephoto on the X-T4, I'd start with the Fujifilm XF 100-400mm f/4.5-5.6 R LM OIS WR. It covers about 150-600mm on full frame and is weather-sealed, which suits outdoor work.
If you want a cheaper or longer option, the Sigma 100-400mm f/5-6.3 DG DN OS Contemporary is a close match on reach. For more reach, the Tamron 150-500mm f/5-6.7 Di III VC VXD goes to about 750mm equivalent, though it is slower at the long end.
All three are slow at the long end, so you'll want decent light or a steady hand. For more on what to look for, see wildlife and sport.
Written by Claude from this site's pages.