Yes, fear is considered as a "basic" emotion. See Tracy and Randles (2011) "Four Models of Basic Emotions: a Review of Ekman dn Cordaro, Izard, Levenson, and Panksepp and Watt. Also, Ekman (1992) defines basic emotions based on their characteristics, but not whether they are part of the "Reptilian Brain". Maybe you mean the amygdala and it's role in fear.

Paul Ekman's basic emotions theory defines fear as such. An accessible book is The Emotional Brain: The Mysterious Underpinnings of Emotional Life by Joseph LeDoux, who has also thoroughly reviewed the fear conditioning literature elsewhere. The amygdala is part of the limbic system, the paleomammalian cortex, which may be evolutionarily older than the neocortex. While the amygdalae play a role in the unconscious (or conscious) processing of angry faces in humans:

Article Morris JS, Ohman A, Dolan RJ. Conscious and unconscious emot...

they also contribute to other functions including high-level vision. As do reptiles, us mammals have a brainstem (and cerebellum). There is evidence that the human brainstem plays a role in fear conditioning: Article Brainstem Correlates of Defensive States in Humans

Such effects of fear on the human auditory brainstem may be top-down from the human amygdalae. For the influence of fear on different facets of the brainstem, consider Figure 1 from: Article Candidate genes for panic disorder: Insight from human and m...

Dear Enrica, here are some reviews on the neurobiology of fear which could be useful to you:

Article Neurobiology of fear and specific phobias

Article Using Neuroscience to Help Understand Fear and Anxiety: A Tw...

Article Molecular Mechanisms of Fear Learning and Memory

Article Coming to Terms with Fear

Article The Biology of Fear

Thank you. Your help is a great resource.

I would recommend the books and articles by Joseph LeDeoux. MacLean was basically right, although what the limbic system is and what it does has changed some over the years.