A close-up of the main branches. Thanks.

If it were mine, I would leave the center portion (trunk/stems and immediate top growth) intact and prune back all the side growth that is affixed to the horizontal trellising. That would allow enough room to replace the trellis, yet ensure enough of the older and larger growth of the clematis so as to avoid shocking the plant.

fwiw, cutting back hard does have limits :-)) If the major trunk/stems are very woody - say larger than an inch diameter - I would NOT recommend cutting back into that hard wood. And that goes for any type of clematis.

Thank you gardengal!

Should I wait until late winter / early Jan to prune i.e. after all the leaves fall off?

Also, I am thinking of, for the side growth, I would just cut the woody branches and leave the non-woody ones and re-attach them to the new trellis. Would that be ok or should I do as you said, just prune back all the side growth?

Thanks again.

Peter.jones - it's a Clematis montana and imo will take any amount of cutting back in our climate. I would let it flower this spring and then cut back hard, either to about a foot high or at the level of the top of the fence. I would then pull down the entire trellis including the clematis rather than trying to untangle it. And then replace the trellis. (If it's yours - which it seems to be judging by the posts being your side - you'll have to talk to the neighbours).

If you do it now you'll lose this year's blooms.

We have one over our stone shed. It has survived the shed being entirely re-roofed and having builders clumping all over it.