Revenge was a desire for retribution.
The Great Intelligence called revenge "a petty human emotion" (HOMEVID: Downtime) although later the Intelligence entered the Doctor's time stream in order to kill him for revenge. (TV: The Name of the Doctor)
The Nemesis told Ace "I am whatever I am made to be. This time Peinforte called me "Nemesis," so I am retribution." (TV: Silver Nemesis)
According to Tzim-Sha, revenge was what every living creature wished for. (TV: The Battle of Ranskoor Av Kolos)
Korst Gogg Thek Lutiven-Day Slitheen sought revenge against Luke Smith for the death of his father. (TV: The Lost Boy)
Before Clara Oswald had been killed by a Quantum Shade, she begged the Twelfth Doctor not to take revenge. He bitterly noted to Ashildr that this had been Clara's way of saving the immortal. (TV: Face the Raven) After spending billions of years trapped in a temporal loop with his grief however, he abandoned this promise, (TV: Heaven Sent, Hell Bent) a Time Lord author speculating that the Doctor's claim of knowing the truth about the Hybrid was an elaborate form of revenge to scare their people in retaliation for killing Clara. (PROSE: A Brief History of Time Lords)
During the Planetary Relocation Incident, the recently orphaned Adelaide Brooke witnessed a Dalek regard her before flying off, inspiring her to travel in space. When the Tenth Doctor questioned if she sought revenge against the Daleks for her parents' demise, she denied it, simply wanting to explore the galaxy. (TV: The Waters of Mars)
In 2066, shortly after Herbert Bittle retired from being a postman, he bit a dog as revenge for the years of being bitten by dogs. Bittle was to appear in court roughly a week later charged with cruelty to animals. (PROSE: Solar Streak A.O.K. [+]Loading...["Solar Streak A.O.K. (short story)"])
During the Last Great Time War, Vassarian was abducted by the Sontarans who used him to develop and power temporal weapons and defences. As revenge, Vassarian manipulated the Sontarans into attracting the attention of the Dalek Fleet so his captors would be destroyed. (AUDIO: The Eternity Cage) Reflecting on the origins of the Last Great Time War, some theorized that it was motivated by a Dalek desire for revenge for the Genesis Incident. (PROSE: The Astounding Untold History of the Greatest Enemies of the Universe)
The Silents planned for humanity to destroy itself as revenge for hunting them for a generation when they left Earth in the 2010s. (AUDIO: In Memory Alone)
The subject line of Missy's threatening email to Ruby Baker was "Revenge." (PROSE: Yes, Missy)
After being freed by Rose Tyler, D'Pau's species enslaved their once enslavers as revenge. (COMIC: Empire of the Wolf)
During the Last Great Time War, an alternate Davros sought to ally with the Time Lords to take revenge on the Daleks for imprisoning him in Falkus. (AUDIO: A Genius for War)
After Adam Mitchell had been evicted from the TARDIS, (TV: The Long Game [+]Loading...["The Long Game (TV story)"]) his mother perished from a brain embolism. Angry at the Ninth Doctor for erasing the future knowledge that could have saved her, Adam began plotting revenge on the Doctor. After securing a vortex manipulator, Adam made contact with the Tremas Master who aided him in his plan to abduct the Doctor's companions. (COMIC: Mystery Date [+]Loading...["Mystery Date (comic story)"]) Adam ultimately abandoned his scheme when he understood that the Master had been using him, threatening to destroy the timeline of the Doctor's TARDIS to create chaos across time, giving his life to stop the Master. (COMIC: Endgame [+]Loading...["Endgame (POT comic story)"])
The Spy Master claimed to the Thirteenth Doctor that he razed Gallifrey out of a desire to "make [the Time Lords] pay." (TV: Spyfall [+]Loading...["Spyfall (TV story)"])