The senior judge was the head of a three-judge panel which deliberated the fate of Ian Chesterton during his murder trial in the city of Millennius. His three-headed bench seemed to have commonality with some appellate courts on Earth of the 20th century, in that the judges could only overturn the sentence — on Marinus, effectively handed out by the police — if there were positive proof that exonerated the accused.
Because the court did not operate on an "innocent until proven guilty" standard with which the First Doctor was more familiar, the senior judge offered to give the Time Lord wide latitude in mounting his defence of Ian. This apparent generosity of spirit allowed the Doctor to dramatically point the finger of guilt at Aydan in open court. Even this was not enough for the senior judge and his colleagues to overturn Ian's conviction. It was only when Ian had minutes left to live that the Doctor was able to offer conclusive proof which the senior judge accepted.
Throughout the proceedings, the senior judge appeared to evince an air of efficiency, fairness, and collaboration, with both his colleagues and the jurists standing before him. (TV: "Sentence of Death")