He will do exactly what he has been doing from Day 1 ― try to “bring everything crashing down.”
He will continue to use his weapon of choice, Breitbart, to attack his adversaries inside the West Wing ― mainly Jared, Ivanka, Cohn, etc. He will relentlessly attack Congressional Republican leadership like Paul Ryan and Mitch McConnell (and Jeff Flake and John McCain). In many ways, I think Steve will feel liberated. Free from the limitations of “serving” or “answering” to somebody. It’s not in Steve’s DNA to work for anybody but himself. He likes being the dictator. Now, he will be able to operate openly and freely to inflict as much damage as he possibly can on the “globalists” that remain in the Trump administration.
If Steve senses that Trump is being co-opted by the Jared/Ivanka/Trump Jr./Cohn base, he (and Breitbart) will turn on Trump and recruit someone else like Attorney General Sessions to replace him. I would think that in some ways, Steve will want Trump to feel the pain of his departure, and it would not surprise me if Breitbart starts playing up more of the things that they’ve avoided touching to this point ― like the Russia investigation.
I think it’s important to keep in mind that Steve’s departure changes nothing about the things that make Donald Trump unfit to be president. It’s Trump who tweets day and night. It’s Trump who has consciously decided to pander to racists and white supremacists. It’s Trump who has engaged in a dangerous game of chicken with North Korea. At the end of the day, while some of the West Wing infighting may calm down, the real root of the problem is in the Oval Office.