Templar Bases, otherwise known as Templar Command Posts, are a hazard in the Shadow Plague DLC. They are the Shadow Plague equivalent of Z COM fortresses, fortifying the countries they are in. They will appear shortly after the popup stating that the Templars are planning to counter the vampire menace.
Take down the Templar Bases as soon as possible. They will only get harder to defeat the more time they are allowed to fortify their countries. There is a possibility that a Templar Base may be created on an island, such as New Zealand. It may be advisable to destroy this Base first. Make sure your Blood Rage is strong, at least up to Shadow Blades if possible, or you will be unable to overcome the Templar Bases. If you can not defeat a Templar Base with a Blood Rage, another strategy is to evolve Shadow Slaves and infect people in the country, as the Shadow Slaves will destroy the Templar Base. Additionally, placing a Lair in the country next to the country with the Templar Base will allow you to have a safe haven nearby, where your vampire can regain health at an accelerated rate and be battle-ready more quickly. Evolving Lair Healing 1 will help toward this.