Varys has a history of being a bit shady (to say the least) and Dany questions his service to her. Varys insists that he's loyal to no king or queen but to the people, which Dany accepts. She asks Varys to tell her in advance if he has an issue with her style of ruling, rather than just secretly plot to overthrow her. He promises, but he later suggests to Tyrion that Dany may have some of the traits her father "The Mad King" had, since Dany can be ruthless in her pursuit of the Iron Throne. He tells Tyrion he better nip that in the bud, before Varys has to step in and be his usual shady self.