Local departments allow you to issue the policies and effects of the palace in your other cities.
Local Department is an Administration Building which affects and boosts buildings built within its street range, which is equal to half of the range of the Palace. The local department requires the Seat of Power DLC, it can be built only in the Old World (and Cape Trelawney), only one local department can be built per island. Constructing the local departments is possible only after building the palace first.
Unlike in case of the palace, local departments can have only one department active and only one policy from the chosen department. Buildings in range are boosted by both the passive effect of the department (depending on the main palace's prestige level) and the active effect of the policy. The department and policy must be unlocked first in the palace. Policies chosen in local departments are independent from the policy selected in the palace, i.e. policies in each local department can be different from each other and from the policy chosen in the palace.