Hi Lucas, you can say don't have a car or haven't got a car, both have the same meaning and you use them to talk about present tense.

Hola Lucas! HAVE can be used as a main verb or an auxiliary verb. For example, "I haven't got a car." HAVE serves as an auxiliary for the verb "to get." As a general rule, we use "do not have" when referring to the negative present tense. Do not follow "have not" with a noun; for example, "I have not a car" or "I haven't a car." Of course, language is often descriptive, not always prescriptive. We Canadians sometimes use, for example, "I haven't a clue." It's mostly an outdated usage, but it can be heard rarely. I speculate that it comes from our British roots. However, as native speakers of English, we use it sparingly if at all - like spice in a recipe. It sounds very awkward if used incorrectly.

IF you say "have not" with a noun, it would be "have no". I have no money. But in regular conversation, one would say: "I do not have a car", "I don't have money" or better "I don't have any money". In these cases "have" is not an axillary verb, it will require an axillary verb (like "do") to form questions and negative forms.