In which serial did the Second Doctor first encounter the Time Lords?

The Second Doctor first encountered the Time Lords in the serial "The War Games." The ten-episode story formed the conclusion of Patrick Troughton’s television tenure and revealed that the Doctor belonged to a powerful civilisation from Gallifrey.

After the Doctor and his companions uncover a scheme involving human soldiers, artificial war zones and alien manipulation, he calls on the Time Lords for help returning the displaced soldiers to their own eras. The Time Lords then place the Doctor on trial for stealing a TARDIS and violating their law of non-interference.

The serial introduced the Time Lords and Gallifrey to viewers, although Gallifrey was not actually named until the 1973 serial "The Time Warrior." As punishment, the Time Lords exile the Doctor to Earth and force him to regenerate, leading into the Third Doctor’s era. The story therefore marks both a major expansion of Doctor Who mythology and the transition between its second and third Doctors.