In trying to recruit an unaware Ryan into joining her in a possible future where she ruled all of the timeline Jia showed her hand too soon. Her future self sent a message that warned her past self of the threat Ryan posed and Clintons' scheming against her. Jia seemed to know Booster Gold who she called by his real name when he arrived to assist the lost hero. Later the Chronos couple showed up as part of the Starro threat against Time Masters. Having no other option Booster agreed to let her go after she helped him and owe her a favor of her choosing. When the crisis was over Booster who had never met her before (though she was already familiar with him) wanted to know her story. Jia used her wiles again making yet another bold statement that they were lovers in her time. Rip Hunter angrily told her that he would never permit that to happen. She kissed Booster much to Chronos' annoyance saying it was just insurance. How much if any is true has yet to be revealed.
Powers: Lady Chronos has an ability she calls Void Time that freezes the victims body making it impossible for them to move much less defend themselves. How she came by these powers, whether they are natural or a product of her costume has never been stated. She likely can not time travel without the Time Watch both her and David Clinton use though she can open portals through time.
Her future?: Jia has told many stories of how things will play out. She has said that David Clinton will be/was her husband, that she still cared for Ryan, that Booster and her were together, etc. Not everything is clear with her, like her referring to Dwarfstar, a fake Atom like hero, as her first born. Whether he is in fact her son is questionable at best. What is known is that at some point in time she will gain control over the timeline only to have Booster Gold and an Atom rebel. Her body was found with Ryans' future corpse appearing to have stabbed him while he strangled her.