The track record of actors off hit prestige television shows is pretty good with the exception of the Sopranos. The cast of Mad Men did very well for the most part, with Slattery loading up on character actor parts, Shipka getting her own show on Netflix, and Harris getting multiple major supporting roles. Big Love turned Amanda Seyfried into one of the biggest stars of her generation. Breaking Bad resuscitated Odenkirk's career, and was able to get a weak actress like Anna Gunn more roles than she deserved post-show.
Even the Sopranos, which I felt picked its cast on looks more than talent, turned Edie Falco into a bankable TV lead and made Jamie Lynn-Sigler into a b level stage and TV star prior to her getting sick.
Game of Thrones is bigger than any of those shows, and I think all the cast will have plenty of opportunities. If I was Emilia Clarke's agent, I would start loading her up with chick flick/date movie roles. She is OK as an actress, but is really likable in interviews and promotions. Date movies are steady work. I think Maisie Williams will be fine. She is probably the best actress of the bunch.