Gaining Renown

Downtime Activity: Gaining Renown DMG p129 A character can spend downtime improving his or her renown within a particular organization (see "Renown" in chapter 1). Between adventures, a character undertakes minor tasks for the organization and socializes with its members. After pursuing these activities for a combined number of days equal to his or her current renown multiplied by 10, the character's renown increases by 1.

Source: DMG, page 129