When something has "run its course," it means that it has come to a natural end or conclusion. Antonyms for this phrase could include "just beginning," "on the rise," "gaining momentum," "in its infancy," or "in full swing." These terms describe situations or events that are just starting and have a long way to go before reaching their full potential or ending. "Just beginning," for example, could apply to a relationship that is just starting, or to a business venture that is in its early stages. Overall, antonyms for "ran its course" suggest a sense of growth, energy, and excitement, rather than a sense of closure or finality.