The phrase "on brink of" can be used to describe a situation where something is very close to happening, but hasn't quite happened yet. Some other synonyms for this phrase include "on the verge of," "at the edge of," "on the cusp of," and "on the threshold of." These phrases all convey a sense of anticipation and excitement, as something important is about to happen. Some other related words might include "imminent," "impending," or "approaching," which also suggest that something significant is about to occur. Whether you're on the brink of a new chapter in your life or simply waiting for a big event to happen, these synonyms can help you convey your excitement and anticipation.