I have printed pictures of the main NPCs and also made sure each PC was connected or familiar with their faction. Each faction has its own agenda so to speak. This helps in the RP aspect and gave the player some framework. For our group, we started from Lost Mines of Phandelver. So at the first meeting, in the waiting area where guards and secondary members where hanging out prior to the meeting, I gave the PCs a chance to mingle.
There they encountered old friends such as Sildar Hallwinter and Daran Edermath from Phandalen that they were affiliated with at low levels. I also introduced rumors and guards from various regions affiliated with the main members of the council. One important rumor I kept dropping was that spies of the cult could have infiltrated the council and the PCs should be on the lookout.
Later on with council session two the PCs where more familiar with the council, I had them investigate the spy side quest, which was suggested in the book with a succubus. The side quest for the council spy led them to a notorious Zhentarium owned bathhouse in Waterdeep. The spy turned out to be non other than Sildar who was under the influence of a Succubus. This ended up being a RP encounter as they once again saved Sildars hide.
My goal was to personalize the council and have the PCs feel connected and more immersed within the council and its actions.