The phrase "close/hard/hot on the heels of" refers to an event that follows closely after another event. It indicates a sense of urgency, excitement, or danger. There are several synonyms for this phrase, including "right behind," "in pursuit of," "on the trail of," "hard after," and "in the wake of." Each of these phrases convey the same meaning, urgency, and excitement. It is often used in situations where there is a need for immediate action, such as in sports games, business deals, or law enforcement. Regardless of the specific phrase used, the message is clear: something important is happening and it needs attention now.