They had different surnames because a younger son (i.e. Alonso III Fonseca) would take the surname of his father (“Fonseca”) and the older son would take the name of his grandmother (the mother of his father the archbishop), which was “Acevedo.” As archbishop, he was forced to confront Condado de Altamira, Count of Altamira, because the count was meddling in the affairs of the Tierras de Santiago, and also put a stop to the injustices committed by the governors there, taking advantage of his close relations with the Spanish monarchy as well as the papacy.

He was also involved in lawsuits against the Benedictine monks of San Martín Pinario, during a resurgence of this religious order in Galicia.

He presided over his father's funeral in 1512, at which Gonzalo Fernández de Córdoba, known as "The Great Captain", attended, and Fernández de Córdoba symbolically offered his weapons to Saint James the Great (Santiago) at the funeral.He assumed the leadership of the Galician nobility, who wished to maintain their privileges, and was named by Charles V as a member of the Royal Council.

Fonseca presided over an assembly at Melide, whose aims for the Kingdom of Galicia included demands for legislative representation and a new board of trade (casa de contratación) based at A Coruña.

Around 1507 the old Pilgrim's Hospital in Santiago de Compostela was purchased with the aim of transforming it into a university college.