Cut it back. It will regrow. And likely quite rapidly, too. I had one in my old garden that I cut back hard every late winter and it would regrow prolifically back to its former size. And random partial diebacks are not unheard of either, even in our mild winter zone.

Thanks Gardengal. Should I completely cut back even the main trunks from the bottom that is holding the top growth ?

Yes, cut everything down to the ground that is not producing green new growth. There is no 'top growth' for the trunks to hold up. Everything in the picture which is not green is dead. Honeysuckle is one of the very earliest plants to show new foliage, so if there is none now there never will be.