While there isn't any confirmation within the book series about Brienne's Clegane heritage (and in fact she actually duels Sandor Clegane in the "Game of Thrones" show), George R.R. Martin himself has already revealed that Brienne is related to another famous warrior.
At Balticon in 2016, Martin revealed that Brienne of Tarth is a descendant of the legendary Kingsguard knight Duncan the Tall, something that is hinted at in "A Feast For Crows." Duncan the Tall is one of the most accomplished knights in Westerosi history and serves as one of the titular characters in Martin's prequel series "Tales of Dunk and Egg." Brienne's true heritage is hinted at when she recalls finding Dunk's old shield in "A Feast for Crows," bearing his shooting star and elm tree insignia, which she then has painted on her own shield.
According to u/juvegirlbe's theory, this means that both Sandor and Gregor Clegane are also related to the legendary Ser Duncan the Tall, which perhaps accounts for Gregor's ludicrous height of eight feet. Though Martin has yet to confirm whether or not the Cleganes are also related to Dunk, this entire theory upends practically everything we know about Brienne's history — connecting her to one of the most evil characters in the series and implying that Duncan the Tall is responsible for Gregor Clegane's reign of terror.
