"Merry chase" is a playful way to describe a lighthearted pursuit, but there are plenty of synonyms you can use to expand your vocabulary. "Frolicsome pursuit" has a similar tone, emphasizing the joy and excitement of the chase. "Capricious pursuit" adds a sense of unpredictability and whimsy, while "jaunty pursuit" suggests a carefree and confident attitude. If you want to emphasize the competitive aspect of the chase, you could use terms like "vigorous pursuit" or "fierce pursuit." Ultimately, the synonym you choose will depend on the tone and context you're trying to convey, but there are plenty of lively and playful options to choose from!