Via Doctor Who TV
Clara can’t meet 10 (or the War Doctor) otherwise all of her episodes become pointless. So does she get her own adventure with UNIT?
Well, presumably the Doctor could meet her and then assume when he eventually meets Clara that he would travel with her – and perhaps that helps him realize that there must be another Clara out there.
But yes, it is hard to do things with multiple Doctors without creating continuity errors. The Five Doctors notoriously has the Second Doctor thinking about how his companions’ memories were wiped when they were taken from him – but the Second Doctor is apparently forced to regenerate immediately after that, and so when is this supposed to have happened? A retconned attempt to fix this is seen in the Two Doctors, which posits that the Doctor was allowed to go on some missions for the Time Lords before his exile to Earth. But it makes little sense.
I just saw a picture of Clara with 10 & 11 & Queen Elizabeth. It’ll be interesting to see how that works out. Hopefully not like the example you mentioned above.