The phrase "were hot on the trail" can be replaced with a variety of synonyms to enhance the meaning of the sentence. Some alternatives include "were close on the heels," "were tracking closely," "were in pursuit of," "were on the scent of," and "were following the lead." These phrases not only add variety to the language but also provide a more vivid description of the situation. It conveys a sense of urgency and excitement that captures the reader's attention. Using a wide range of synonyms allows the writer to keep the reader engaged and creates a more immersive reading experience.