You asked

Best portrait lens for the sony a9 iii?

For portraits on the a9 III, I'd start with a fast telephoto zoom, since it gives you room to step back and keep the background soft:

Whichever you pick, the light will do more than the lens. Put your subject near a window, turn them a little, and expose for the face. See portraits and light beats gear.

Written by Claude from this site's pages.

From these pages