Well, this is all going to be an educated guess, since we don't know exactly what rose it is. But, since it's growing up a trellis my guess would be that it's a climber, and you don't need to prune climbers much in the spring.

I prune climbers by just shortening the secondary canes to a few inches. The primary canes are the biggest longest ones that form what you could call main branches, and the secondaries are the smaller canes that grow off of those. The secondaries are the ones that flower, and are the ones you trim. You don't trim the primaries except when they're getting too big for the space.

All roses are fertilized later in spring, when they have a few inches of new growth on them. If you are going to spray with fungicides, you start as soon as the leaves first come out.

Wait until it blooms and then post a picture here. People will help you identify it and provide advise on how to care for it. If you can't post a picture just describe blooms color, fragrance leaves, thorns, etc. We will be happy to help
I am in MD close to VA and unfortunately my experience is that a lot of climbers that survive here without special care and come with houses are rootstock that is used to graft other roses, Dr Huey. Hope this is not your case.
Sometimes there is also New Dawn.
Olga

Can you ask the former owner of your house which rose it is and how to care for it?

Connie