If possible move or transplant the Clematis in the early spring, just as the green leaves began to appear.
Clematis roots can go as deep as 4feet, so dig up as many of the roots as you can.
Use a large nursery pot to hold the plant until you can relocate it.
On a personal note, I needed to move a Clematis attached to a decking--while it was in bloom.
Though the plant did take 2 years to recover, it survived the move and is a lovely specimen in my garden.