The job of shepherd and the job of king couldn't be more different from each other. Shepherds are on the lowest rung of society, kings are at the top. But God says, through the prophet Ezekiel, that the Messiah will lead in a way very different from earthly authorities who lord it over their people and cause harm with their poor leadership.
Our King takes on the job himself. Christ, like a shepherd, will give rest, seek out the lost, bring back the strayed and scattered ones. He will heal the wounded and bind up the injured. He does not delegate, but will "shepherd them rightly." We have a king who cares for us and who is not afraid to "judge between one sheep and another" (Ezekiel 34:17).