Hello!
The cane (the part with the leaves) is done growing, but should live on for some time still (a few years, at least)- new growth will come from the base of the cane - this type of orchid is sympodial - meaning it sends up new growth from along a rhizome, rather than continuing to grow upwards - blooms generally come from mature, or very nearly mature canes. The canes will with time drop their foliage, but should remain green and plump (wrinkling a bit with age) and firm, and continue to support the plant to grow more, so you don't want to remove old canes unless they are dead. You can cut off the bloom spike when the flowers are spent.
The plant looks good - will most likely need more light to rebloom -some of this type MAY rebloom on previously bloomed canes, but more likely, won't bloom again til new growth has matured - likely around the same time next year.