Antonyms for "taking precedence" include "being secondary," "having less importance," "being subordinate," "taking a backseat," "being less urgent," and "being less significant." These words describe situations where something is not given as much priority or attention as something else. Examples of this might include a lower-priority project, a less urgent need, or a subject matter that is of lesser importance. When something is not taking precedence, it is often considered to be of decreased relevance or value. In contrast, taking precedence means that something is more important or urgent and should be prioritized over other tasks or concerns.