Ummm…he was in the front part of the ship that made it through the slipspace rupture. He was at Chief’s memorial at the end of Halo 3 and flew off back to the Elite homeworld, I believe.
Look it’s been 5 years since Halo 3, but you can’t have forgotten how in the very ending he was standing on Earth, with Lord Hood etc
the Dawn got ripped in 2 halves, one went through the portal (the front piece, with arbiter), and when the portal closed the back half (with chief) was left behind, floating in space
To be more precise, the Arbiter is on Sanghelios trying to bring together all of the Sangheili. After the Prophets were gone, the Elites pretty much reverted to the way their society used to run. Kind of like ancient China/Rome.