After leaving the Dark Space, Klaus decided to spend some more time on Planet Blue Jade, specifically to meet and talk with the Jade Queen.
Since her attempt to make Klaus her disciple failed, building a different kind of relationship benefits them both. Klaus is a rising star, so he will need places to hide out if need be.
From what he had seen on Planet Blue Jade, he knew for a fact that even against Celestials, provided he could get there, he would be safe.
So he made sure that the connection was established.
He also spent some time with Princess Evren. She is a disciple of the academy, so they are bound to meet there one day.
Klaus learned that soon, the 64 academies in the Human Universe would hold a tournament to determine the best academy and top disciples. She had no plans on backing out, but she also didn't want Klaus to not join.
According to her, she would train hard and become a demigod to enter the main event and compete for a spot on the Rising Dragon List.
