Yerin can only advance while fighting powerful foes and there aren't many of those left. There's like... 8 underlords from the tournament, a handful of powerful underlords over 35, then literal emperors and senior members of monarch families. She needs to be contrived into a major conflict or there's no path forward.
Even if Lindon made it to the top 8, she had to go further in the tournament I think.
Yerin could train with the other sword sage if she were out early but I don't think she can truly go forward until the next conflict happens (probably a war or some kind after the tournament) or in the tournament itself. Lindon on the other hand seems to be able to progress in different ways.