- You may be looking for the cartography practice from which this street derives its name.
The trap street was under the jurisdiction of the immortal human Ashildr, working as mayor of the camp under her alias "Me". Hidden from public notice by a misdirection circuit, it existed at the heart of central London. The entrance was a narrow passageway located between two buildings on a major street in the city. The trap street strongly resembled a 19th century streetscape.
The street provided refuge and sanctuary for a variety of alien species - the Twelfth Doctor was able to identify at least "27 different species on [the] street... 15 of whom [were] known for aggression." Despite the presence of individuals from war-like races such as Sontarans and Cybermen, no conflict was permitted on the street; at the time of the Doctor's first visit, there hadn't been a single act of violence on the street during the last century.
The law of the street was very strict; crimes such as murder or theft were punishable by death, a sentence handed down by Ashildr and enforced by a Quantum Shade with which she had made an alliance. Upon entering the street, individuals would be captured by a force field so that the residents of the street could assess them; any humans who had inadvertently entered the street, or any aliens whose claims for santuary were deemed insufficient, would be dosed with Retcon to erase their short-term memory and ejected from the street.
Ashildr came to reside on the trap street around the time of the battle of Waterloo. She became the street's mayor.
In the early 21st century, Rigsy was summoned to the street via a call to his mobile phone; once there, he was framed for the supposed murder of Anah. Sentenced to death by Ashildr, a chronolock was placed on him, and his memory was erased. Waking the next morning and remembering nothing of the previous day's events, Rigsy contacted Clara Oswald to ask her help in uncovering the source of his "new tattoo".
The Twelfth Doctor, accompanying Clara and Rigsy, was able to track down the trap street in spite of its misdirection circuit. Once they had entered the street, the Doctor and Clara focussed on investigating the truth behind Anah's murder; Clara, unbeknownst to the Doctor, encouraged Rigsy to pass the chronolock on to her. This mistake would later lead to her death.
With the help of Anahson, the Doctor discerned that Anah was not actually dead - the entire crime had been fabricated as part of a ploy by Ashildr, who had previously made a deal with the Time Lords to capture the Doctor in exchange for the continuing safety of the street. After Clara was killed by the Quantum Shade, the Doctor was transported away from the street by means of a teleport bracelet. (TV: Face the Raven)
After escaping his confession dial and arriving on Gallifrey, the Doctor had the Time Lords use an extraction chamber to remove Clara from her timeline the moment of her death on the trap street. It left her body processes frozen between one heartbeat and the next, but ultimately, Clara's death was a fixed point in time; she would have to return to Gallifrey, and then be returned to her own timeline, or risk damaging the very fabric of the universe. After stealing her own TARDIS, and picking up the still-living Ashildr from the end of the universe, Clara confirmed that the Time Lords could return her to the moment of her death on the trap street. However, as she was theoretically immortal due to the nature of her current condition, Clara decided to return to Gallifrey and thus her death on trap street "the long way around", and first set off for more adventures with Ashildir in her own TARDIS. (TV: Hell Bent)