One of the main Servants contracted to the Main Character.
A beauty who hides her smug demeanor and venomous tongue behind a relentless smile. Her nickname is “Casko.”
She is a Japanese-style Servant, and as her Caster class might suggest, she primarily uses spells.
Her demeanor is often cutesy, and she likes to refer to herself in the third person, using phrases like “Tamamo-chan” (“the adorable Tamamo”).
Her dream is to become the Main Character’s wife. Although she dreams big when it comes to the MC, she can be quite the merciless realist when it comes to anything else.
While she admits that she can occasionally be a bit air-headed and preoccupied with romance, she is fundamentally a realistic and rational being whose words strike to the heart of a matter. According to Nero, “Tamamo hides her true depth behind her lewd facade.”
The truth is Tamamo is a Divine Spirit class Anti-Heroic Spirit.
She has lost her true power, so in Extella she is of similar level to normal Heroic Spirits. But as the number of her tails increases, maxing out her spirit level, her power grows beyond measurement, exceeding the realm of human perception and understanding.
This is only expected, since she was originally revered as the embodiment of the Sun itself, and as such her existence carry a similar weight.

In the beginning of EXTELLA, she saves the Soul of the Main Character, who had relied on her to escape. While the Main Character sleeps, Tamamo gains a general understanding of her new environment, including the state the Main Character is in and the meaning behind the Regalia. Despite this knowledge, she decides to pretend to not know anything, secretly making use of the Regalia to carve out her own domain, while acting as if she were the only Servant the Main Character ever had. She is a very efficient woman.
When Archimedes comes to her, she instinctively realizes that he is up to no good, but ignores her instincts in order to spend more time being lovey-dovey with the Main Character.
This is how Tamamo becomes the monstrous Empress of her kingdom.
She follows her whims, and not only forces her perspective on the Servants who serve under her, but on occasion uses her influence (power) to pressure even the Main Character to ensure she gets her way.
Tamamo no Mae is typically sweet and affectionate towards the Main Character, but will turn cold and cruel at the suggestion of peaceful negotiation with others, chiding him or her for questioning her methods, all through a threatening smile. “When you show such unnecessary kindness to others,” she might say, "I might find myself upset. Even I have no idea what I might do.”
It goes without saying that her goal is not to achieve peace on SE.RA.PH, but to return the Main Character to normal, and keep him or her by her side until the very end.
She can see plain as day that Archimedes is lying, so she plans to use this knowledge to her advantage, and come in and “save the day,” capturing the Main Character’s heart in the process.
But an evil empire isn’t built in a day, and evil deeds are bound to come back to bite.
Ultimately, she admits her misconduct, and decides to fight for the Main Character’s goal of saving Altera.
Nero is motivated by a pure desire to save Altera, but Tamamo, who can discern Altera’s true nature, better understands the risks involved in pursing such a course. However, she approaches the situation with a predictably in-character attitude, caring more about her “Husband’s” choices and accomplishments than about the well-being of the galaxy.
She WILL destroy the Umbral Star. Altera can be freed along the way. She’ll plant her foot on the faces of Archimedes and Corroded Liz.
Above all, no matter what happens, she will support the Main Character.
That is the way the day-dreaming fox, the “good wife” Tamamo, lives her life.

Fate/EXTELLA material: Encyclopedia of Fate EXTELLA