Only by being accepted as a Direct Disciple by an Academy Teacher can one be promoted to a Confucian scholar and wear the Jade pendant.
Thereby becoming an official member of the scholarly classes among the various schools of thought, fully acknowledged by their respective affiliations.
However, many students will not be selected because there are few Academy Teachers to begin with, thus slots for disciples are limited. Those not chosen can only wait another year to participate in the next Teacher Apprenticeship Ceremony.
But there are only three chances, for those who have not become scholars within three years will leave Linlu Academy, and a new cohort of students will arrive.
According to Li Jinsu, Zhao Rong doesn't need to worry about being forced to leave Linlu Academy after three years. Because of that recommendation letter, this 'Connection Disciple' just needs to stay out of trouble and he'll be taken in as a Direct Disciple by Teacher Yan within three years.
But still.