Ancient emperors placed great importance on the matter of establishing an heir.
Tips
register
嗣 is a classical/literary term rarely used in everyday modern speech. It most commonly appears in historical texts, legal documents about inheritance, or compound words like 子嗣 (heirs/offspring).
memory
The character combines 司 (to manage/oversee) and 冊 (records/scrolls) — the one who manages the family records is the designated heir.