When Halo 3 ends, we can see a great alliance form by the UNSC and the Elites supporting the Arbiter.
The next game after it, is Halo:ODST; I played a long time ago but I do recall that there was no presence whatsoever of the arbiter nor the elites, in fact all your enemies were Grunts, Jackals, Hunters or Brutes.
Later in Halo 4 the elites are back, but like my enemies, I don't recall anybody mentioning the Arbiter. What happened here? Where's the Arbiter?
ODST occurs shortly after Halo 2, before Halo 3, and it's on Earth. I don't think the rebel Elites are present, simply because the rebels aren't on Earth yet at that point.
We don't see the Arbiter in Halo 4 because at the end of Halo 3, the Arbiter and fellow Elites headed off into the sunset to find their homeworld (source link).
Chronologically Halo 3: ODST is concurrent with Halo 2. Elites do not show in that game because the ones left in New Mombasa were killed by Brutes in preparation for the Great Schism (the conflict between Brutes and Elites seen in Halo 2).
In Halo 4 your enemies are a Covenant remnant faction led by Jul 'Mdama who seeks to finish the extermination of humanity. Jul is of the opinion that humans will hold a very severe grudge against Elites and seek genocidal retribution in the future. Thel 'Vadam (the Arbiter) doesn't enter into the story in Halo 4 but he does still lead a powerful Covenant remnant faction which is a de facto ally to the UNSC.
From Halo: Glasslands:
The Arbiter made sense. There had been a time when the San’Shyuum had made sense, too. Jul wondered if he could actually speak up now, but the words formed and suddenly he could hear his own voice filling the chamber.
“What do you plan to do about the humans?” he asked. “Gods or no gods, they’ll return to their colonies and rebuild them, and they won’t forget what we did to them and how much they loathe us.”
“We’ll consider that if and when it happens.”
“Instead of finishing them off before they regain strength?” There. It was out in the open now. “We should regroup now, while their guard’s down, and exterminate the threat once and for all. Unless you’re too fond of them as pets, that is.” The chamber was horribly silent now. Jul could suddenly hear the slow shuffling of boots as elders squirmed. He expected Thel ‘Vadam to round on him, but the Arbiter just snapped his jaws together a couple of times in amusement as if there was something he should have told Jul but chose not to.
“The humans say that a fool does the same thing twice and expects things to turn out differently.” ‘Vadam lowered his voice. “It might have escaped your notice that we never managed to defeat them, and we’re in worse shape now than we were a year ago.” Then his expression changed, as if he was steeling himself to break bad news. “We’ve stopped fighting. We need to stop because we can’t rebuild without stability. I plan to reach a peace agreement with the humans, to formalize what has already taken place. Both sides have finally run out of blood to shed, brother.”
As for where the Arbiter is during Halo 4 the likely answer is Sanghelios, the Elite homeworld. He has been trying to rebuild a functional nation there since the Human-Covenant War ended.
The EU (the one novel i can think of is called "The Thursday War") says that while the Arbiter's forces-the ones friendly with the UNSC- are the dominant power on their home world, they face domestic insurrection from splinter groups. The largest splinter group, the Covenant Remnant, is the primary antagonist in Halo 4.
The elites in Halo 4 are still in a civil war on their home planet against the other covenant. It is unknown who the leader of the Covenant that are fighting against the Elites are after the Prophet of Truth is killed by the arbiter in halo 3.The arbiter is still Incharge of the Sanghelli. Although, some Sanghelli didn't believe in the arbiters statement that the Forerunner artifacts shouldn't be touched. Those elites left the arbiter and went to Requiem. This group of Sanghelli is called the Storm. The storm is led by Jul'Mdama. Otherwise known as the "Didacts Hand."
The Arbiter and the Elites (and grunts) that broke off from the Covenant will return in Halo 5: Guardians. The Arbiter will be a playable character during part of the campaign, as he was in Halo 2. The story will explain what has happened in the time between the last appearance of his faction of Elites.
