Some plants may be more affected than others, as there can be variation between plants. Leave them be and they may produce some new growth, this can be a slow process. Dead-looking branches should not be removed until there signs of new growth on the plant to demarcate dead bits. If the frost penetrated the main stem, the whole tree might die.
I have 6 olive trees which seem to be dying. They have plenty of water and are sheltered in a 15 ft wide side garden. Some seem to be dead while others have buds and leaves varying amounts on each. They have been in the same spot for 6 years but this year they are in trouble. Can you please help as they were expensive. They are about 5ft high.
This is probably caused by frost. Olive trees are not reliably hardy and while they are grown outdoors in mild coastal areas with a reasonable expectation of survival, this diminishes significantly further inland. The last decade had seen very little hard frost in winter, but last winter was the coldest for 18 years in some parts.