You can trim this Clematis back, as most foliage is already done for the season. Leaving a few vines with green is a fine idea, if you can separate them. Leave the plant about waist-high, and cut back further after threat of heavy freezing. I do it when the buds swell but before leaves really open. You can reduce each branch to a few sets of buds at that time.
It’s critical to keep the area around the base and root zone free of weeds and grasses. After you weed, a layer of organic compost will support the roots and inhibit weed seed sprouting. In the spring, trap or treat for snails and slugs around the stems.
“Most clematis will perform better with an annual pruning. Those that bloom during summer on new wood need heavy pruning in winter or early spring, or they will look thin and stringy. The kinds that bloom in the spring on last year's wood can do without pruning, but are better if cut back lightly after they have finished flowering in the later spring or summer.” The quote about pruning is from this OSU Extension article. Though you have an established plant, much about how to plant and care for a new one still applies.