The Arbiter acts as the primary enemy of the game, charged with the destruction of humanity by the Prophet of Regret. He is ultimately killed by the marine John Forge in a climactic battle at a Forerunner installation.

What happens to the arbiter after Halo 3?

At the end of 3, the last we see of The Arbiter is at the memorial site, talking to Lord Hood about the presumably dead Master Chief. Both characters are under the impression that Chief had died. Arbiter goes to his ship and goes home, and that's the last we see of him.

How did the arbiter survive Halo 1?

It is possible he escaped in a drop ship and floated around Halo's debris field until more cruisers showed up; which wasn't very long after Halo's destruction. That's what Johnson and a few survivors did before they met up with Chief & Cortana in the Longsword ...