There are two main ways you can move your HQ in Rogue Assault; in War Zones, and Between War Zones
MOVING IN WAR ZONES
For the most part, players are able to move to any hex in a War Zone free of charge, but doing so will place you on a "Movement Cooldown". The farther you move your base, the larger that Cooldown will be, while it is active you will be unable to move your base again until it expires. That being said, players can speed up that Cooldown with "Movement Cooldown Tokens". Much like the farther you move the longer your Cooldown will be, the more time left on your Cooldown, the more Movement Cooldown tokens you will need to speed it. Movement Cooldown Tokens can currently only be earned via your daily login crate, and the free crates found in the Black Market.
MOVING BETWEEN WAR ZONES
Moving to a different War Zones can also be done free of charge and also places you on a Movement Cooldown, but unlike moving in a War Zone, this cooldown is always 1 hour, and can not be sped up even with Movement Cooldown Tokens. That being said, this is a separate timer than the Movement Cooldown applied for moving in the War Zone, so while you won't be able to move War Zones again for another hour, you can move around in your new War Zone if you wish.