Answer: Usually it is a good idea to trim a plant back to remove seed pods and conserve the plant's energy. This would tidy it up and also encourage rebloom if it is a rebloomer. Without knowing specifically which plant you have it is hard to make suggestions as to how to care for it on the long term. (Some for example do better with a hard pruning after the spring bloom flush.) In my experience most of the plants commonly called jasmine can be overwintered in a bright but cooler room to help them set buds for spring. Here is an article you might find interesting, it demonstrates why I am not sure which plant you have!
I'm sorry I can't be more specific for you.
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