Here is an example of what I mean by "internal logic." In existing Narnian stories, we find that the population of the Narnian world is small enough that, in war, even a force in the hundreds can be significant. In "The Horse and His Boy," Rabadash leads a force, as I recall, of only two hundred. Compare this to King Nero's tournament in your story: there are enough participants that JUST finalists would number a thousand. There could have been more than five thousand warriors beginning the tournament--and logically there would have been still others BESIDES those. This means that Nazar must have a large population, maybe bigger than Calormen. If Nazar is that big, and has existed for a hundred generations, you need to be thinking WHY Nazar was NOT involved in "official" past history. When Jadis was ruling Narnia, did she have a treaty with Nazar?
For fan fiction to be good, you do need to think about harmonizing your new elements with what was already there.