It is something that April had done in why Harrison is doing in what he doing. Most likely Harrison was part of the group that the Klingons were supporting. He might had been the son of that group leader. April most likely had hurt or cost the death of that leader.
The aliens April and the Klingons are supporting are insect-like, not human. So, that's unlikely, unless the movie will suggest that April and the Klingons pitted a bunch of difference races against one another.
Anyway, there is a line spoken by someone (an Admiral) in the recent preview that suggests Harrison is a "Starfleet Commander", whatever that is supposed to mean.