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彼女からは警戒心が剥き出しの刺々しい雰囲気はない
In this sentence, 刺々しい雰囲気 appears as the noun here and being modified by 警戒心が剥き出し. But how could a complete sentence like 警戒心が剥き出し take the particle の to modify another noun? It would make sense if 警戒心が剥き出しの刺々しい雰囲気 is a complete sentence, but there is はない in the end, which means 雰囲気 must be the main noun being modified here. Wouldn't it be more correct if it's something like
彼女からは剥き出しな警戒心の刺々しい雰囲気はない?
But how could a complete sentence like 警戒心が剥き出し take the particle の to modify another noun?
Remember that Japanese has something called a "double subject" construction such as 彼は背が高い, フランスはワインが有名だ and この本は表紙が緑色だ. By pulling out the は-marked argument and leaving the が-marked argument, you can construct a relativized phrase like so:
Your sentence is basically an example of this. 警戒心が剥き出しの is a perfectly valid adjectival (noun-modifying) expression, and it modifies the following noun phrase 刺々しい雰囲気. (Note that むき出し is a no-adjective on its own, and Japanese adjectives are similar in syntax to verbs.)
To explain this in more detail, 彼女は警戒心が剥き出しだ is a valid sentence but (この)雰囲気は警戒心が剥き出しだ is not. I think this 警戒心が剥き出しの is a gapless relative clause that modifies (刺々しい)雰囲気. Similar examples include:
