You asked
Can I adapt the sigma 500mm f 4 dg os hsm sports to nikon z?
I can't confirm that. The Sigma 500mm f/4 DG OS HSM Sports page lists only Canon EF and Nikon F mounts, and none of the cameras it fits are Nikon Z bodies. I don't have adapter details, so I won't guess whether an adapter would work or how it would perform.
If you want a 500mm for wildlife on a Z body, look at the Sigma 500mm f/5.6 DG DN OS Sports. It's a comparatively light 500mm prime, and I'd start there for a mirrorless setup. For the broader picture of long lenses for fast-moving subjects, see wildlife and sport. If you want to try a focal length before committing, buying used explains why good lenses are an easy way in, since they hold their value well.
Written by Claude from this site's pages.