One thing I've always wondered is how could a single supernova threaten the entire galaxy? In VOY, they witnessed dozens during the Q Civil War and the galaxy came through the ordeal just fine.
Anyways, as for the empire. I would assume that the Senate would have evacuated and re-established themselves on another world within the Empire. There would be a period of instability, when disgruntled worlds conquered by the Romulans would try to break away and the Klingons may try to claim some new territory.
After that I would see them sealing their borders for the third time to rebuild in private, reestablish their control and let things settle down.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)