She travels a lot. She [visited/ have visited] many countries.
In "she travels a lot," the present tense has an enduring aspect. She'd done a lot of traveling and we expect her to continue doing that. Thus the present perfect "has [not have for the third person] visited" is an excellent match as it covers time past all the way up to the present. On the other hand the simple past, "she visited," indicates that she's completed her visiting, which is at odds with the first sentence.