I think that if you only need to move it three feet, I'd train it sideways away from the gate rather than dig it up and move it.
I'm with Dove on this one, wouldn't risk moving it unless I absolutely had to.
I agree. Just remove, or tie in stems that are in the way of the gate and train all others away from it. Newt spring when new growth starts, train it in the direction you want it to go, away from the gate. You have time bteween now and then to provide it with extra framework to support it if needed.
Moving a clematis 3' is pointless and success cannot be guaranteed as they have such deep, fleshy roots and are hard to dig out without doing serious damage.
Has Break23 'Ignored' me?