IIRC, there was only one preist of Mithra, in the original stories, that displayed any magical abilities. The fact that he had been dead for over a thousand years may have had something to do with the degree of magic he was able to weild. Even then all he really did was, allow Conan to astral travel to the location of his grave and enchant Conan's sword so that it could damage a demon from the Outer Dark. Both rather small spells from a D&D standpoint.
Most of the magic users in Howard's works, Conan and others, are more intrested in the use of power to further their own goals or the goals of those that they serve. Rarely does a preist/wizard appear that uses their power for the general benefit of humankind.
Looking through the Scholar class in the preveiw, I would say that any preist of Mithra who has magical ability got it through one of two methods.
1, Before becoming a preist, the character learned magic through one of the other backgrounds and developed this ability as time went on. During the course of the character's life they had an experence that convinced them to turn to the preisthood as a way of life. Going through the course of their iniation they decided to set aside those spells and knowledge that would conflict with their vows and focused only on the abilities that, they feel, would serve Mithra and the beliefs that their faith supports.
2, Early in the character's life, they felt the calling to join the preisthood. Going through the required studies and learning of the history of those who went before him, the character feels a stronger and stronger conection to Mithra and those preist who established His worship in the lands. This conection allows the preist to summon up their faith and display it through acts of magic. Since this character is using magic based on their belief and faith in their god, he/she would be unable to consider using it, in normal situations, for anything other then the glory of Mithra and the betterment of those who follow the same faith.
How a character comes to be able to use magic is a matter of which background they chose and the player's concepts of where the character is heading. In most cases this will be something that they will need to talk to their GM about and make sure that it matches with the style of game the GM plans on running.
One correction. As I've been typing this I recalled a second preist of Mithra that used magic. However, this character left, was thrown out of, the temple for misusing his abilities and showing an unnatural interest in the darker arts. After leaving, he spent additional time in study and became proficant in the dark forms of magic.