I don't think that the Empire will have disappeared entirely. Will it have changed? Absolutely. Will it have shrunk? Lost some Provinces to independence? Maybe.
All I really know is that the political landscape will have drastically changed with no strong heirs to the throne from the Septim line. Think about that. As much as the populace may have hated/loved the Septim line, they were the image of stability. For over 200+ years, no one but a Septim sat upon the throne of Tamriel (there was the Jagar Thorne situation of course, but that was an aberration in my book). How did the Empire change in the intervening 200 years leading up to Skyrim? Who were the candidates for the new Emperor? How viciously were the battles for ascension to the throne?
Did Morrowind get completely taken over by Black Marsh? Did the Dunmer fight back and reclaim at least their Ancestral Lands and retain Morrowind as its own Country/Province? How much (if any) of Skyrim, High Rock, Sommerset, Black Marsh, Morrowind, etc, seceded from Imperial control and became their own Sovereign Nation again?
If the Empire shrank some but is still a relatively strong influence, would the Aldmeri Dominion attempt to put their plan for conquest of Tamriel into high-gear?
These are most of the questions I look forward to reading about in the canon/lore-books in the new game. I think that this story-line (and the history that is almost necessarily involved in it) is going to be the best one yet.
Tamriel that we know of so far:
Aldmeri Dominion Controlled:
Summerset Isle
Valenwood
Black Marsh Controlled:
Black Marsh
Morrowind (Yes it was completely taken over, not to mention reduced largely to ruins by the explosion.)
Independent:
Elsweyr
Cyrodiilic Empire:
Cyrodiil (may have lost parts to the Aldmeri Dominion. I don't remember.)
Hammerfell
High Rock
Skyrim
I'm not positive with the others but please correct me if I'm wrong but I think that's the current situation. As of Skyrim there is a civil war breaking out between rebels that want Skyrim to secede and loyalists that want Skyrim to remain a province.
I think if the Empire is stable after Skyrim with the provinces I listed there could easily be an uneasy "cold war" of sorts between the Cyrodiilic Empire, Black Marsh, and the Aldmeri Dominion. The only motives known for sure are those of the Aldmeri Dominion: a "purification" of Tamriel to build a dominion to serve Altmer interests.
Again correct me if I'm wrong but I think that's what Tamriel looks like according to the most recent lore.