An apology was an expression of one's regret for wrongdoing, usually conveyed by saying "sorry".
Rose Tyler apologised to Queen Victoria for her "nakedness". (TV: Tooth and Claw)
K9 Mark 2 gave Starkey a dog whistle, which would call the robot to his side, as an apology for nearly killing him when he mistook the human for a Jixen warrior. (TV: Regeneration)
Vincent van Gogh apologised to the Eleventh Doctor and Amy Pond for the clutter in his house. (TV: Vincent and the Doctor)
Kate Stewart offered the Eleventh Doctor the official apologies of UNIT after the TARDIS was transported by helicopter. (TV: The Day of the Doctor)
The Twelfth Doctor started using apology cue cards due to his sometimes colder traits to get him out of tight situations. (TV: Under the Lake, Face the Raven)
Gaspard de Saux-Tavannes apologised to Catherine de Medici after he mistook her for Simon Duval. (TV: The Massacre)
Daleks did not accept apologies. (TV: The Stolen Earth, AUDIO: Extermination)