According to secret information found by the Spy Master in the depths of the Matrix, the First Tecteun was a Shobogan and one of the first inhabitants of Gallifrey to explore other planets. After becoming the foster-parent of the Timeless Child, a mysterious being whom the Master believed to have eventually become the Doctor, they extracted the regeneration code from their Child, splicing it into their own body and into other Shobogans'. In the process, Tecteun became one of the Founding Fathers of Gallifrey.
The First Tecteun allegedly became the first of her kind — the Shobogans — to explore outer space. (TV: The Timeless Children) Other accounts suggested that the dominant humanoid species of Gallifrey was known as the Gallifreyans, and that they were already a well-established space empire long before the discovery of regeneration and time travel. (PROSE: The Legacy of Gallifrey)
At any rate, still according to the Matrix records shown by the Master to the Thirteenth Doctor, Tecteun discovered the Timeless Child on one such planet on the far edge of another galaxy, and adopted the foundling as her own. For a time, the two travelled the universe in Tecteun's spaceship as mother and daughter. (TV: The Timeless Children)
When Tectuen and the Doctor were reunited, both having regenerated several times, the Doctor was mad at her adoptive mother for robbing her of her life, as there were all sorts of explanations as to why she was alone at the vortex entrance. (TV: Survivors of the Flux)
Back on Gallifrey
Tecteun eventually brought the child back with her to Gallifrey. When Tecteun discovered the child's ability to regenerate, she experimented on several of their incarnations to discover the secret to this ability to the point where it became an obsession of hers to find out the mysteries of regeneration. Eventually she injected herself with the genes which had been spliced from the child. Upon doing so she immediately regenerated into a male incarnation. (TV: The Timeless Children)
Tecteun's first incarnation had the appearance of a light-skinned woman with long dark hair, initially seeming to be middle-aged when she discovered and adopted the Timeless Child. She spent many years studying her foster child's regeneration power, and grew old in that time. By the time of her first regeneration, she had become elderly, with her hair turning grey. (TV: The Timeless Children )