13th Division, Defensive Tactics & Seireitei Protection
The 13th Division is the ones that actually send out patrols on a daily, frequent basis to survey Seireitei. If a threat occurs, they find and take care of it, sometimes with help from other divisions. They also work together with various divisions.
If a threat is a large enough, the 13th Division is in charge of sending out shinigami, assembling them, assigning them duties, and other things. Their job is similar to the 10th, except on a smaller basis.