First Tecteun

According to secret information found by in the depths of the Matrix, 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 explorer
In her original, female incarnation, 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)

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)

A new body
As the Shobogans grew in power and technology, Tecteun became one of the leading figures of the new society, based in the newly-built Capitol. He gave the new generation of Capitol-dwellers the regeneration code, but decided to limit the "common man's" regeneration cycle to a maximum of twelve regenerations. Tecteun had laid down the base of the society which would soon rename themselves the Time Lords. (TV: The Timeless Children)

Secrets in the Matrix
At some point after the Timeless Child's memories were redacted and the child became the Doctor, Tecteun hid the truth in the Matrix disguised in the story of Brendan, an immortal Irish Garda. suggested that Tecteun hid the truth in this manner as an apology or gift for her child and a way for the Doctor to decode the truth if they so chose. (TV: The Timeless Children)

First incarnation
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)

Second incarnation
Their second incarnation had the appearance of a younger, dark-skinned man with short hair. When he became one of the founding members of Time Lord society he began to wear a white version of the common Time Lord robes and headdress. (TV: The Timeless Children)

Relationship with other Founders
Tecteun bears resemblance to Thremix, who was a Gallifreyan biologist behind regeneration in The Scrolls of Rassilon. However, she also becomes the first Gallifreyan to regenerate, an honor that was Rassilon's in The Legacy of Gallifrey. In the scene corresponding to the point in The Timeless Children where Tecteun's second incarnation stands alongside two other Time Lords in full high-collared regalia, the Timeless Children script release mentions that "we can assume [the other two] are Rassilon and Omega". This confirms that, as far as Chris Chibnall's authorial intent was concerned, Tecteun is not an alternative name of Rassilon or Omega as had been proposed by fans following the broadcast of Series 12, but rather a third member of a triumvirate of Gallifreyan founders. The "third founder" alongside Rassilon and Omega was already a highly mythologised figure in Doctor Who lore, with many stories referencing a mysterious third founder known as "the Other".

The Cartmel Masterplan was predicated on the idea that the Doctor was the Other, or a reincarnation thereof, an idea later confirmed in the novel Lungbarrow; in some way, the story introduced in The Timeless Children splits this conception of the Other in twain, having the Timeless Child be the forgotten earlier self of the Doctor who existed in the days of Time Lord society's genesis, but having the third forgotten founder be their adoptive parent.