This guide is based on info about the Provost I found here: https://wasteland.gamepedia.com/The_Provost
After freeing the Provost from the Warrens (see related achievement guide)
you can take him to the Snowed Inn Resort and you can fix the toaster found down the rightmost path (the one before the gates). Inside will be a Token of Minerva, which will cause the Provost to engage you in a conversation (in Latin, of course). He will eventually say "Minervae autem noctua custos, coniungere nobis. Venite ad cor montis." (Guardian of Minerva and the Owl, join us. Come to the Heart of the Mountain). So he is inviting you to the heart of the mountain. Travel to the new location named Mysterious Cave marked in the north-west of the world map (extreme corner). If the Provost is with you, you will see the end of his hidden side quest, you will gain a new perk and a new achievement of course.
Tips for the Provost:
He is an uncontrollable companion but doesnt follow you everywhere. Sometimes he disappears but when you enter a new area he is there again. He doesnt engage in combat that often, he has a decent small arms weapon and enemies seem to ignore him when the full team is not incapacitated. So dont worry about losing him.