Hand of the King: Olenna. You need someone clever, capable and politically shrewd as Hand.

Grand Maester: Samwell. Smart, trustworthy, dedicated.

Master of coin: The former Head of the Iron Bank. Whoever they are, they've got to be good with money in order to have reached that position.

Master of law: Tyrion. Same reasoning as blackmage.

Master of ships: Davos. Has experience with ships. Is awesome.

Master of whisperers: Varys. Great at his job, has the kingdom's best interests at heart.

Lady Commander of the Kingsguard: Brienne. Brave, honourable, loyal, and undoubtedly one of the best warriors in the Seven Kingdoms.