Spiritual

Spiritual, or Ecclesiastical: To do with the next world, or in reference to God or the church.

A spiritual or ecclesiastical authority would be a Bishop, an Archbishop, a Pope and so on.

Note that the spiritual authorities can't kill anyone, even if they are a heretic, a witch or similar. Thats what temporal authorities are useful for. So, after condemning a person for heresy or witchcraft, a spiritual court (eg: the inquisition) would hand over the accused to the temporal authorities for execution, etc.