One of my climbers that I moved 2 years ago is only now growing new canes. I thought the climber was dead.
First, prune back the climber by about 2 feet. Then cut out all diseased and old wood. Then dig it up making as wide and deep a hole as possible so as to not disturb the roots. Have your new hole prepared already with aged manure bonemeal and organic topsoil. Plant the rose in the new hole and water in well. Keep well watered. Don't expect your rose to do well in the first year after you move it. It will take a while for it to become accustomed to its new home. But after that it should do well again.