Easy.
They knew all along that they were gonna run out of books at the last seasons, BUT they had the characters well defined, and the whole plotline. So you hire some pro screenwriters WAY BEFORE reaching the 'no more books' point and you make them prepare the story in detail. That way, when you reach that point, you don't find yourself suddenly lost.
It's not that difficult: scifi and fantasy writers have often worked with secondary authors. I'm thinking now Terry Pratchet, Orson Scott Card, Asimov (to name a few). Usually, the main writer (the famous one) defines the main events, characters and plotline, and the secondary writer does the hard work and fills the details. HBO could have used RR Martin's info and hired some ghostwriters to prepare the missing areas in advance.
HBO had several years to prepare it BEFORE reaching this point and realizing they didn't know what to do.
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