From the game's encyclopedia
The Request Anointment Character Interaction is a special interaction that can be used by a Ruler of Empire Tier or higher on their Head of Faith, or clergy Head of Rite when there is none, to secure their support in an Anointment.
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.
Request Anointment is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "The Request Anointment Character Interaction is a special interaction that can be used by a Ruler of Empire Tier or higher on their Head of Faith, or clergy Head of Rite when there is none, to secure their support in an Anointment." It is part of anointment. Patch 1.20.1.2, from game/common/game_concepts/ach_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/ach_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.