remove the dead side and dust/paint the cut with a fungicide. they sell it at garden centres I think it might be called arbotex. someone on here will know. if not then they should at the gc.
the live side should carry on as normal.
and welcome to GoY too :o)

from the photo it look as if the other trunk is going the same way.

Thank you for the replies - yes I did fear the worst cliffo - but can't bear the thought !

If you 'listen again' to GQT on radio 4 22 Jan on the BBC iPlayer, there's a useful discussion about large wisterias. Apparently they are tough as old boots and will cope with 'heavy' pruning.