Bald wisteria

We inherited a well established wisteria 2 years ago when we moved house. It flowered well last year but this spring we have had buds, which have opened fractionally, but have had neither leaves nor flowers. We have a new shoot which has appeared about 4’ from the main trunk which has lovely fresh leaves. Is the original wisteria likely to bloom next year or should we cut back all the old wood and encourage the new growth? We live in Cornwall and did get snow during the beast from the east spell but everything else in the garden has survived. Any advice would be appreciated.