Bring a small saucepan three-fourths full of water to a boil over high heat. Add the garlic, return to a boil and cook for 3 minutes. Add the carrot, return to a boil and cook for 1 minute more. Drain, then plunge the garlic and carrot slices into cold water. Drain again and peel the garlic (the skins will come off easily).
Transfer the garlic and carrot slices to a glass bowl. Add the olives, onions and gherkins and mix well. Add the olive oil, vinegar, salt, chili powder, pimentón and thyme and stir gently to coat all the ingredients evenly. Cover and refrigerate the olive and vegetable mixture until well chilled, at least 2 hours or up to 6 hours, stirring once or twice.