If Gendry had managed to escape the cart in season 3, it would have drastically changed the storyline for him. He would have been able to avoid being captured by the Brotherhood Without Banners and subsequently handed over to Melisandre. This would lead to him not being used as a sacrifice during the leech ritual with Stannis, and the possibility of him being taken as a hostage by Robb Stark's forces. Without being a prisoner of the Brotherhood, Gendry would also not have formed a bond with Arya Stark, and their friendship would not have developed. This could have significant implications for Arya's character arc, as her experiences with Gendry and the Brotherhood helped to shape her as an independent and capable fighter. Furthermore, Gendry's escape would have prevented the reveal of his true heritage, which was a major plot point in later seasons. If he had not been captured by Melisandre and was able to make his way back to King's Landing, he could have potentially tried to claim the Iron Throne himself as the rightful heir of Robert Baratheon, which would have added a new dynamic to the political landscape of the story.