The outdoor training grounds within the castle walls were for the average soldier. Any soldier of any class could train there as much as they desired as long as it didn't get in the way of their other duties.
However, inside the castle, there was a training area for the higher classes. Varya had used it when she took self-defense training and Galen often took Basil Jr. there when he tried to teach him how to conjure up and control his aura.
That day, Galen was there without the child and shadowboxed in the empty gym, somewhat happy to be alone. He felt that maybe it would be peaceful enough at the end of his training session to meditate.
It was a couple of hours before Varya would need him and he knew that the prince had likely stayed there so her safety wasn't an issue for him at that moment.