From the game's encyclopedia
The leading Character of a Rite: the Head of Faith if they follow it; otherwise the holder of the Clerical Region where the rite has its strongest following, and failing that, the Ruler who governs the most of the Rite's Counties.
Only the Head of Rite may edit their Rite's Tenets and Doctrines, and it is they who speak for their flock when the church drifts toward Schism.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Head of Rite is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "The leading Character of a Rite: the Head of Faith if they follow it; otherwise the holder of the Clerical Region where the rite has its strongest following, and failing that, the Ruler who governs the most of the Rite's Counties." It is part of Rite. Patch 1.20.1.2, from game/common/game_concepts/pam_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/pam_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.