Ah, the Law and Order detective genre shift in that one League system (that I want to sat bomb to the ground for their insolence).
On the League planet, you need to talk to people at the comms and visit the bar for unusual... stuff.
In the same system, you need to talk to people at K. Starworks (the pirate planet where player can raid for blueprints, but don't raid now!)
Visit Groombridge space station in the same system for clues.
Maybe try hacking the comm relay?
Eventually, you need to talk the archon again after you gathered enough evidence.