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Clara herself isn't a paradox but she has been involved in paradoxical events. Many -- but not all -- of those events resulted from her entering the Doctor's timestream in "The Name of the Doctor", which caused a large number of "echoes" of her (we don't know just how many) to appear throughout the Doctor's history. She also participated in the events of "The Day of the Doctor", wherein the Doctor crossed his own timestream multiple times & changed his own history by saving Gallifrey, instead of destroying it. On top of all that, in "Hell Bent", she was extracted from her own timestream a moment before her death (in "Face the Raven") & took to travelling with the immortal Ashildr (a.k.a. "Me") in a stolen TARDIS. Not only is that itself paradoxical but it also gives her ample opportunity to become involved in further paradoxes.

Look at Eleven's Entire life as a whole, and you'll soon see many paradoxes with Clara. Nine and Ten didn't really have a paradox - the events of their lives aren't actually changed by Gallifrey being Saved. But Gallifrey being saved produced effects for the Doctor... Effects that are paradoxes themselves.
Eleven's first year: The Cracks in the Wall, they're there from the TARDIS exploding. Why did it explode? The Kovarian Chapter of the church of Silence/whatever sought to prevent him from getting to Trenzalore. Why were they preventing him from getting to Trenzalore? Because that is were one of the Cracks - caused by the TARDIS explosion (predestination paradox) - is located, and being used by Gallifrey to ask 'the oldest question in the universe'. But they're supposedly destroyed. But the Doctor would never answer, no, the reason they tried to stop him getting there is because that's where he supposedly died.
He Didn't Die because, (drum roll), Clara saved his life. (by pleading to Gallifrey to help him). But heres the thing, The only reason Gallifrey could save him, was because she convinced him, Ten and War Doctor not to destroy Gallifrey. An event during which one of his future Regenerations (twelve) arrived to assist in. Meaning that the only way Gallifrey could be saved, is if they had saved him....
Now work our way back again. Without Gallifrey Saved, That Crack at Trenzalore wouldn't have a message. Without that message of Gallifrey origin causing fear etc, the Doctor would never go there, and so the Kovarian Chapter would never try to blow up the TARDIS...
Now lets work forward again... back to Clara. Clara only had the doctor's number because of Missy (The Master's future regeneration after escaping gallifrey after Ten's 'End of Time' special), while he was only intrigued by her, looking for her, because he'd already met her, witnessed her death twice. Sort of for the first one.
How had he met her? Dalek Asylum. Genius enough to hack the Daleks' pathweb. That Clara Died, and then he met another one victorian london, Great Intelligence's attempt at making a physical body, it (the body) killed her. Both are Paradoxes of their own, as they are both echoes of Clara. How? Dalek Asylum, a ship breached the shield crashing... sole survivor, one genius. Without her being there, the Daleks would never have known - it was her 'transmission' that got the Dalek's attention - and he never would have gone there. (bit of a theme). Victorian London, he'd just lost Amy and Rory, well, not just, but was basically wallowing and Vastra and Jenny had to take care of him. There was issue, the Great Intelligence and co, and he only got involved because an Echo managed to pass an impossible test. To Tell the Doctor the problem, and WHY he should get involved, with one word only. "Pond." The What is easy, but how would she have known that 'pond' would work? unless... yeppers. Paradox. Without Clara there...
Which brings me to how she got there. The Impossible girl who was his companion because she'd already saved him. She got to those through a scar... entering his own timestream, on Trenzalore. Because he died there. But because of Clara, he didn't... so how could she have spread echoes of herself throughout his history to save him? And I dont just mean that she didn't need to as the Great Intelligence also wouldn't have gotten to go back (hence why she needed to save him), I mean there are clear events where her interference had the big step of making her own travels and presence on Trenzalore that day possible.
But then, that's why she's the Impossible Girl.