In Fire Emblem Three Houses as soon as you get to the Monastery you’ll find that you’ll be earning Renown Points. These points are a type of currency that can be used in the Monastery to upgrade your character in the Cathedral.
Within the Monastery you’ll find four statues in the northern Cathedral area on the first floor. These four statues will be where you spend these Renown Points, with each statue giving you different perks for spending Renown. The statues aren’t available right away, you’ll actually need to complete a couple of story missions before they become available. Then you’ll need to speak with the Saint Statue Artisan to spend points there.
But first, you’ll need to complete a side mission called Tending to the Saints. Once you complete the mission, the Saint Statue Artisan will allow you to spend your Renown at the Saint Statues in the Cathedral of the Monastery. These quests and NPC will occur after you’ve completed the “Assault at the Rite of Rebirth” mission where you get the Sword of the Creator.
Many of the activities that you’ll do around the Monastery will be rewarded with Renown Points. In fact, many of the activities like side quests, fishing, and others will net you Renown for completing them as well as Professor level points.