The 9th Division prevents information from leaking, as well as information being stolen. Their shinigami work close with the 8th Division research facility, to protect it from outside influence. They also prevent important information from leaking into Rukongai, especially information that could cause an uproar or mass panic.
Adding to this, they are also in charge of dealing with tactics and warfare against intelligent beings and massive hollow gatherings, and are the ones responsible for any counter tactics when Seireitei is under attack.
9th Division is also in charge of the memory-replacing that has to be done after shinigami fight in the living world.