I'm pretty positive that no king is around in TP, Zelda sits on the throne and she is the one who has the power to deciede wether Hyrule should be slaughtered or covered by Twilight.
It could however be that the king has died during the invasion of Zant, since Zelda and the few guards seem to be located at the castles last resort. He might have fallen in battle and thus the ruling power goes to Zelda. This would also serve as a good explanation as to why she is still revered to as princess, there was no time for a offical crowning.
Well, no prove but it's still fun to ponder.

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