In ‘Day Of The Doctor’ Clara meets the War Doctor and 10th Doctor and asks the 11th Doctor if they are both him. The 11th Doctor is puzzled by this as Clara had encountered both in ‘The Name Of The Doctor’. Now the very idea is surprising to her when she has met every incarnation.
Clara claims that she does remember a bit but it very much seems like she doesn’t. It is a small moment that is quickly glossed over but could have greater significance, especially in your own campaign.
The simplest explanation is that when Clara splintered into different incarnations, each saving a different Doctor none of them were the true Clara. She doesn’t retain any of their memories.
This raises the question of which Clara the Doctor rescued at the end of ‘The Name Of The Doctor’. The assumption is that this Clara Prime, the template from which all others were copied from. Yet even this version saw the echoes of the other Doctors, including the War Doctor.
We don’t know the process in which the Doctor retrieved Clara. Was she reintegrated or was she left diminished by the experience? Is the Clara that emerged just a shade of her former self? It could be that her memories fade over time but for the moment she is covering up this fact.
This could be similar to how the various Doctors don’t remember their encounters with each other during this story. Clara has crossed her own time stream and once she emerges the memories begin to vanish.
The rewriting of the universe, first with the Great Intelligence killing the Doctor in the past and then Clara saving him, could lead to unforeseen consequences. Just as the universe was previously rebooted the Clara that emerges could be one that now never had those adventures.
Her first encounter with the Doctor could have been in the tomb of the TARDIS. Maybe this Clara played along, as everyone treated her like they knew her. She could have picked up enough knowledge to pretend to be her former self but occasionally, as shown here, those cracks show.
This might explain why when we next see her here she has become a teacher. This Clara was more academically minded. No longer a child minder she completed her studies and found herself a new job.
We might also imagine that this is a Clara from a universe without the Doctor. Her deception could be based on desperation. She remembers a horrific reality in which the Time Lord wasn’t there to save the Earth from the monsters. This Clara might simply be desperate to prevent the Doctor finding out her true nature and forcing her to return to her own reality (if such a thing were possible).
Yet the Doctor expects this Clara to remember her experiences. This suggests either he didn’t know what would happen once he rescued Clara or there is something else at play here.
‘Day Of The Doctor’ is about Zygons replacing people. There is a small gap between Clara escaping into the past and her rescuing the Doctors that she could have been replaced.
If she was a Zygon it does raise the question of why she didn’t prevent their escape of reveal Elizabeth’s deception. This can be explained if we accept that this Clara-Zygon wanted to see how events played out and would have stepped in if they’d done anything to foil their plan.
As it is she was present in the room when the Doctors ensured that both the humans and Zygons wouldn’t remember their true nature. The Clara-Zygon could have been similarly effected. Even without the real Clara present she might still not know what she was.
This would mean that the real Clara could be elsewhere, a prisoner of the Zygons. She might be trapped in the Elizabethan era, waiting for the Doctor to come rescue her. The Zygons might have placed her in a 3D painting and hidden her away. This could provide a quest for the Doctor once he realises what has happened.
The alteration could have occurred even earlier. Jumping in to the Time Fracture was obviously having an effect on Clara’s mind. This could have left her vulnerable to the influence of the Great Intelligence.
Rather than be destroyed the Great Intelligence could have merged with Clara. He could have access to her personality and some of her memories. He might even be overwhelmed, submerged beneath Clara’s mind.
This would mean that Clara was unknowingly harbouring the Great Intelligence while it healed. Occasionally it rises to the surface but since it doesn’t have total control it doesn’t always remembers the things she should.
The 11th Doctor might have realised this by ‘The Time Of The Doctor’ hence periods in which he travels with different companions (such as Handles). The reason he sends her back home twice might not be to protect her but to keep his compromised companion from such a delicate moment in galactic history.
Over time the Great Intelligence might assume control. It might engineer acts of sabotage without Clara realising or subtlety push the Doctor into situations in which he is vulnerable. All it would have to do is wait for the Doctor to need his life saved by Clara and have her walk away.
This would prove a problem for the Doctor. He’d need to defeat the Great Intelligence but also find a way to save Clara. Luckily we know he has access to methods of memory removal which could erase the presence of the Great Intelligence.