There are several plants that go by the common name of trumpet vine, or variations of that name. One of the most common in New York State is Campsis radicans, a vine with flowers in the red or orange color family and has compound leaves.  There are pictures on this USDA page. 

This plant is native to the  Eastern and Central United States including New York state,  and not considered invasive in the state or the Hudson Valley. It is however, an aggressive grower that takes a great deal of management to control. 

You are not legally obligated to remove the one that you have already growing, but it requires a lot of work to keep it under control.  It spreads by suckering underground runners and the seeds that fall from its pods, and the runners may send shoots up in places where you won't notice them.  It freely self-seeds and can choke out many plants that get in its way; you can never let this plant get the upper hand or be allowed to spread as much as it wants to.  It should be severely pruned back in early spring or fall to just a few buds, and you should deadhead the pods before the seeds can drop.  Pull up the new shoots from the runners whenever you see them.

It needs some support, as it can grow up to 40 feet long, but you should keep it from climbing on anything you don't want damaged. One of the benefits of this vine is that hummingbirds love its beautiful flowers, and other birds like to nest in its dark green foliage.  It can be a lovely plant, as long as it always knows you're the boss.

Courtesy of NYBG Plant Information Service