The following is my summary of events that took place during the reign of Pope Leo the Great, which Martin Jugie examines in greater detail in his study “The Roman Primacy in the East at the Time of St. Leo the Great.”
During the reign of Pope Leo the Great, the pro-Chalcedonian Archdeacon Aetius was removed from his position in the church of Constantinople by the his patriarch, Anatolius. He was ordained the priesthood but exiled to manage a remote cemetery, which was more of a demotion than an elevation. He was replaced with Deacon Andrew, who advocated for Eutychianism.
Pope Leo the Great was informed by his nuncio that Anatolius deposed Aetius and immediately ordered Patriarch Anatolius to restore Aetius to his former position of prestige. He also wrote to Emperor Marcian and asked him to ensure his demand was met with swift obedience. Anatolius desired to be on good terms with Pope Leo, so he asked the emperor to ask Pope Leo to consider him favorably since he acquiesced to the pope’s demands concerning Aetius and excommunicated Andrew.
The patriarch bowed to the potestas of the Pope and assured him in a letter that he would never “make opposition to the orders which had been given” to him by the pope and would immediately “conform to the desires” of the same. The patriarch even took the opportunity to assure the pope that he did not support Canon 28 from Chalcedon, which encroached on the territory of Alexandria and its position in the taxis. He assured him that the canon is not valid because “its efficacy and its confirmation have been reserved to the authority of Your Holiness.”
Moreover, before the same patriarch had been elevated to the his position he showed Eutychian sympathies, having been ordained by Dioscorus. Upon his elevation, he did not clearly affirm the Council of Chalcedon in his profession of faith that was sent to the pope. Consequently, Pope Leo sent his delegates to Constantinople and demanded that Anatolius affirm Cyril’s letter to Nestorius in front of the clergy in Constantinople. When the legates arrived, there assembled a council in the year A.D. 450 and the patriarch assented to the popes demands for a clear confession of orthodoxy.
From these events involving Aetius, Canon 28 and the confession of Anatolius, it seems that Pope Leo the Great was acknowledged to be able to interfere in the affairs of the East, exercise supreme authority over canons from an ecumenical council and safeguard orthodoxy in the East.
 Epist. 132 Anatolii ad Leonem.