Lord or Lady Cardinal (Cardinal for short) was an office of the High Council of the Time Lords of Gallifrey (DW: The Deadly Assassin, et al). The Cardinals were the highest ranking members of the various Chapter Houses of Gallifrey.
Somewhere between Under Cardinal and Cardinal there appears to have been the rank of Junior Cardinal, a rank held by Borusa at the time of the Morbius crisis. (Warmonger)
There was also a sub-office to Cardinal known as Under-Cardinal (BFA: Neverland).
During the future war with The Enemy there appeared to have been War Cardinals. (PDA: The Quantum Archangel, EDA: The Taking of Planet 5)