The Greyjoys are a prominent feature in A Feast for Crows - just one of the reasons it's the weakest in the series - and the focus of their story is the aftermath of Balon's death, and the Kingsmoot (or Queensmoot) that follows. Essentially, this is the various claimants to the Throne - Euron, Asha, Victarion, and a few other Iron Islanders - making their case to replace Balon. It goes on quite a while, and it seems the show are either cutting it or doing a very streamlined version, which is definitely a good thing, and the end result is that it's Euron who wins by promising to conquer all of Westeros for the islanders. After this, he styles himself as the King of the Isles and the North, is recognised by the islanders as such, and begins to rule and make good on his promises.