When Agaburry was very young, he was afraid to climb the trees of his homeworld. His parents encouraged the young Wookiee to persevere as they climbed with him, teaching him a valuable lesson on bravery.
Burryaga joined the Jedi Order and became the Padawan of Jedi Master Nib Assek. In 232 BBY, Agaburry and his master participated in the rescue effort to save the Hetzal system during the Great Hyperspace Disaster. He was the one who discovered that several of the hyperspace anomalies bearing down on the worlds of the system were starship fragments with people still alive onboard. While Jedi pilots attempted to destroy the starship fragments, Burryaga felt the survivors' terror so deeply that it radiated through the Jedi Force network. Facing a language barrier, the other Jedi believed that they were feeling Burryaga's own emotions and initially attempted to remove him from the network. Burryaga's efforts ultimately made the other Jedi realize that the starship fragments had survivors aboard.
A year after the Great Hyperspace Disaster Burryaga and his master Nib Assek attend the Republic Fair on Valo. During the Nihil attack on the fair, Burryaga helped where he could.
Burryaga was on Starlight Beacon when the Nihil sabotaged the station. He became trapped on the bottom half of Starlight Beacon and later discovered, with his friend, Bell Zettifar, the body of his master, Nib Assek, who was attacked by a Nameless. During the evacuation of the lower half of Starlight, Burryaga went missing while fighting a rathtar and was proclaimed dead, though he had actually survived. Bell felt sure that his friend had survived and resolved to find him. Bell remained on the planet of Eiram and mounted a search, eventually succeeding after many weeks in finding his friend.
Burryaga dislike social gatherings due to the fact that most people could not understand him. However, when he was onboard the Galactic Republic medical frigate Panacea with the many patients from the Legacy Run, he was able to help comfort the human boy Serj Ukkarian.
Burryaga wielded a blue-bladed lightsaber with a physical crossguard on the hilt.
Burryaga Agaburry was created for the Star Wars: The High Republic publishing project. He appeared in the 2021 novel The High Republic: Light of the Jedi by Charles Soule. He is described as a "very sensitive Jedi" and wields a blue crossguard lightsaber, with the crossguard design being inspired by Arthurian myths, such as the sword Excalibur.