I'd say that Clara is already a recurring companion. She doesn't live in the TARDIS and travel with the Doctor continuously; she lives at home and leads her normal life, and the Doctor occasionally drops by to whisk her off on an adventure and get her back in time for tea. She's not even a proper companion, since she hasn't committed to the life. She's just a friend.
Indeed, Amy and Rory were the same way in their later tenure -- moving on with their life, with the Doctor occasionally dropping by to whisk them away from sanity for a while. Which made it all the more ridiculous that they had to be "killed off" altogether in some big dramatic ending, instead of just drifting away from the Doctor and mutually deciding they should move on with their own lives.
I always regretted that the classic show so rarely brought back old companions. The only times it ever really did were in "The Five Doctors" and "The Two Doctors." The Brigadier came back a couple more times, but he was never technically a companion. Harry Sullivan came back in "The Android Invasion" (along with Benton), but that was only two months after his tenure as a companion ended. Other than that, it pretty much never happened. Well, they did try to give Sarah Jane and K9 a spinoff, but it didn't get off the ground.