The phrase "be on the track of" refers to the act of searching for or pursuing someone or something relentlessly. There are a number of synonyms for this phrase, including "be in pursuit of," "be in search of," "be hot on the trail of," "be close to the scent of," and "be on the scent of." Each of these phrases conveys a sense of determination and persistence in one's efforts to locate or capture something of interest. Whether you're searching for a lost pet, tracking down a criminal, or hunting for treasure, being on the track of your goal requires focus, patience, and a willingness to follow the clues wherever they may lead.