What do I have to do before I get the alert for Kira to return?

Play through to the end of Onslaught. After you complete the Meridian Complex flashpoint as part of the story and have the custscene on the fleet station you are sent to Onderon to have a conversation with Kira and Scourge. For all characters except the Knight Kira and Scourge will join you as companions after that conversation. Knights they get extra alerts and cutscenes.

You can also summon Kira from the terminal in your Odessen base, if you don't want to wait.

Play through to the end of Onslaught. After you complete the Meridian Complex flashpoint as part of the story and have the custscene on the fleet station you are sent to Onderon to have a conversation with Kira and Scourge. For all characters except the Knight Kira and Scourge will join you as companions after that conversation. Knights they get extra alerts and cutscenes.

 

The problem is that after you complete Onslaught and run the Meridian Flashpoint, the cutscenes play through but there is no additional content past that. It's hinted at by Scourge and Kira Carsen that Satele Shan has led a team to the Emperor's final weapon (his physical body) and that Satele Shan and her crew have become infected or something like that and their ship was sent on an orbital path but has become lost.

 

I've seen youtube videos where players have been able to run through that mission but when you go to look for it, there is nothing to allow you to access that mission. The final cutscenes play out like some sort of cliffhanger.