After he met with the City Lord, Cedric became even more inspired to train more.
This is due to the opportunity given to him. He didn't want to disappoint his guarantor when the time came.
Being admitted to the Starlight Royal Academy was a once-in-a-lifetime opportunity for any Superhuman. Even participating in the entrance examinations could broaden their horizons so Cedric wanted to be at his best form once it was time for him to take the exams.
It wouldn't be now though...
The minimum requirement to participate in the Starlight Royal Academy's Entrance Exam was to possess their token, which is already a difficult process in itself. They also wouldn't accept anybody who hasn't reached Tier 3 Lv.1 at least, they also wouldn't accept those who have already reached Tier 5, so even if Cedric had the ability now, he wouldn't be granted access to it.
