What kind of bush? And what if anything has happened on the living side recently? And what season is it where you are? Raspberries are not a good substitute for the missing half of a bush. They tend to be just a bit too aggressive for ornamental plantings. Maybe an annual vine like cypress vine or some perennial sweet peas would look good in that spot.
This may sound radical but, if you like the bush and it is otherwise healty. cut the other side and trim it down to the main stems and let it grow back evenly. If it is a fast growing bush it may take a couple of years.
Otherwise, why not just replace it instead. Most vines will kill the other side of the bush anyway.
Happy gardening in Hawaii. Gardens are where people grow.
If you have hard soil and a max of one hour sunlight, raspberries won't do well. I don't know of very many vines that will do well in hard soil and little sun, except honeysuckle or Virginia creeper but both of those are weeds you don't want in your yard.