While the timelines shift throughout this play, the bulk of it seems to take place just before The Invasion of Time, as the Doctor has already begun constructing K9 Mark II.
The Z'nai were last heard in The Catalyst, in both the main story and the framing story. In the former, Leela meets the son of the Emperor glimpsed in this story.
Joshua Douglas, who the Doctor traveled with in an earlier incarnation, and who Leela met in The Catalyst, is also briefly seen. He seems to be with the Third Doctor, a man with white hair and a bright red jacket.
In Empathy Games, the Doctor recalls witnessing a world burn, a long time ago. That moment is illustrated in this tale.
The wood paneled secondary console room was destroyed in Empathy Games.