Across the plaza from the Puerta Santa is the long, stark wall of the Mosteiro de San Paio de Antealtares, founded by Alfonso II for Benedictine monks to look after St James' relics, and converted to a nunnery in 1499.
Climbing the steps at the top of the plaza you'll find the entrance to the convent, above which stands the beatific figure of the 10th-century Galician child saint San Paio, his throat being slashed in reference to his martyrdom in Córdoba. Keep an eye out for the sacred art museum, containing the original altar raised over the Santiago relics.