While War For The Planet Of The Apes' Nova may have the same name as the character from the 1968 original, they're not supposed to be the same person. Tim Burton's 2001 remake of Planet Of The Apes was meant to kick off a new series, but while the film was a financial success it's weak critical reception combined with the response to its bizarre twist ending, meant a follow-up didn't happen.
The franchise was rebooted once again with 2011's Rise Of The Planet Of The Apes. Rise dealt with a scientist played by James Franco who raises a hyper-intelligent chimpanzee named Caesar. The film charts the beginnings of the intelligent ape society in the original series and the gradual downfall of mankind. Andy Serkis played Caesar and would reprise the role for Dawn Of The Planet Of The Apes and War For The Planet Of The Apes, which were both directed by Matt Reeves (The Batman). The trilogy, on the whole, received critical acclaim for Serkis' performance and tackling mature topics in a summer blockbuster.
War For The Planet Of The Apes wrapped up Caeser's story and laid the groundwork for the world to evolve into the one seen in 1968's Planet Of The Apes. War For The Planet Of The Apes also introduced a young, mute human girl called Nova, who Caeser has to reluctantly protect while he seeks revenge against Colonel McCullough for murdering his family. The ending to Rise features the outbreak of the Simian Flu Pandemic that wipes out most of humanity, with War revealing the flu has evolved to make humanity revert to a more primitive state. This is why Nova can't speak and the reason McCullough wants to kill those infected.
Of course, Nova is also a mute adult character in the original Planet Of The Apes, making some fans wonder if the young girl seen in War For The Planet Of The Apes is intended to be the same person. This would be tricky timeline wise since the original takes place 2,000 years in the future, but the Nova found in War was never intended to be the same character. The movie itself contains plenty of nods to the original franchise, like McCullough's group dubbing themselves the Alpha and Omega, which references the underground, nuclear bomb-worshipping mutants of 1970's sequel Beneath The Planet Of The Apes.
In the same way, War's Nova was intended by Reeves and writer Mark Bomback (The Umbrella Academy) to suggest history repeats itself in bizarre ways. The entire trilogy has this motif with Rise being something of a remake of 1972's Conquest Of The Planet Of The Apes, where Roddy McDowell's Caeser also leads an uprising. The inclusion of Nova in War For The Planet Of The Apes is not only a reference to the first movie but also another way to suggest the conflict between humanity and the apes will - tragically - cycle and repeat again.