"The Imperial Senate will no longer be of any concern to us. I've just received word that the Emperor has dissolved the council permanently. The last remnants of the Old Republic have been swept away."
From the beginning of the Galactic Empire, Palpatine sought to remove the Senate. The first reason was symbolic: he could not leave a reminder of the Republic. Despite the Imperial Senate being very different from the Galactic Senate, it came to be known as the "last remnant of the Old Republic." The second was political: some senators still opposed him. His obedient majority tried keeping them in check; they understood they were only there to prop up the illusion of democracy. Some, however, didn't understand the sham; they actually tried passing laws against the Emperor's wishes. He dealt with the outspoken ones when they appeared, but like weeds others sprouted in their place. Some of them, as Palpatine suspected, were providing the Rebels with funds, information, and resources.
Warrants were issued for the arrest of all suspected Rebels. Stormtroopers burst into the Senate, and hundreds were detained. Some—those learned to have had Rebel affiliations—were never seen again. The following morning, the remaining senators, unaware of what had happened, came to work only to find themselves locked out of their offices and chambers. Some tried to appeal to Palpatine directly, but were told that their diplomatic access to the Imperial Palace had been suspended "for the duration of the emergency."
Many who were released left Coruscant for their homeworlds, and a peaceful—and isolated—retirement. The small number of senators that remained, the ones who had most voraciously upheld the party line, were generously rewarded with their lives and new positions. Many of them donned ornate jeweled robes and joined the swelling ranks of Imperial advisors.
"...To better protect our citizens and our member worlds, the Emperor has superseded and suspended the Imperial Senate for the duration of this emergency. The Moffs and the Grand Moffs will now have direct control over their systems until such time as the danger has passed. We are sure you shall all do everything in your power to assist us during this time of crisis."
"That's impossible! How will the Emperor maintain control without the bureaucracy?" "The Regional governors now have direct control over their territories. Fear will keep the local systems in line. Fear of this battle station."
Though it was claimed that the dissolution was temporary, only the most deluded of people actually believed the Emperor's statement. A new pyramidal structure was imposed, with himself at its summit, then the Grand Moffs who ruled Oversectors, then the Moffs who ruled sectors, then the governors of individual systems. All of them owed their careers to the Emperor and gave him their allegiance.
The end of the Senate left the field wide open for COMPNOR to step in. For all the power of the Moffs, COMPNOR stood behind them, more powerful still. In the absence of the Senate, Palpatine had established an environment where even his subordinates were capable of terrible atrocities against sentient beings. Behind them all was the Death Star, a weapon that was used to incite fear and terrorize those unfaithful to the New Order.
Organisations such as the Trade Federation that had been puppet governments to the Empire since the Clone Wars had ended were dissolved along with the Imperial Senate. This event had ultimately not only resulted in the disbandment of the Senate, but also the Alliance officially becoming a separate galactic government from the Empire.