Game concept
Primary Heir
The game also links it as Primary Heirs, Primary Heir's.
From the game's encyclopedia
The Primary Heir is the character who will inherit the Primary Title of a Ruler on Succession. This is usually — but not always — the same character as the Player Heir.
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.
Primary Heir is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "The Primary Heir is the character who will inherit the Primary Title of a Ruler on Succession." It is part of Heir. The game also links it as Primary Heirs and Primary Heir's. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.