The phrase "be an adjunct of" means to be subordinate or secondary to something else. The antonym for this phrase would be "to be independent" or "to be autonomous". When something is autonomous, it operates on its own without being controlled or influenced by another entity. Additionally, independence implies that someone or something is self-governing and able to make its own decisions. Therefore, if someone or something is not an adjunct of something else, they are able to operate and make decisions on their own, without being limited or affected by external factors.