As griselinia are slightly tender, I would think part of it has been killed off, I would take some cuttings from the part that is still alive, and remove the whole plant as it,s unlikely to recover very much and as you say would be a bit unsightly.
You can take heel cuttings now through to september, put them in a 50/50 mix of peat and sharp sand and put them in a cold frame, next spring pot them up into 3" pots of john innes no 2 and plunge them outside for the summer, overwinter them in a cold frame, and plant out in their permanent position, the following april. derekm

If the inner bark of the lower part of the stems has been damaged by cold air last winter, they might grow in the spring, but the plant will eventually discard them because they won't be sending sugar to the roots for the benefit of the whole plant. The damage may only be showing up now.