Aaron Begins Priestly Service with Offerings for Himself and the People
Aaron's first day on the job begins with a sacrifice for Aaron himself. Hebrews later points to exactly this weakness in ordinary high priests and says Jesus is different: he has no sin of his own requiring sacrifice.
Where this fits in the story: Leviticus 8's seven-day installation is the explicit narrative prerequisite; 9:1 begins “on the eighth day.”
Where Scripture takes it next: Hebrews 5:1–3 — very strong/explicit conceptual interpretation. The high priest is obligated to offer for sins, for the people and also for himself.