This is a great question. Can we really overcome the fear of death? Even though we as Christians hold on to the blessed hope revealed in the resurrection of Jesus Christ, in our flesh it is difficult to overcome this fear. We are always half-hearted worshipers of the God we love and truly hold on to. Because of that, there will always be a part of us that has these fears. But the difference is that we do not have to let this fear completely paralyze us. Deep down in us, we know that we are going to be with the Lord and that we are going to enjoy eternity with him. That death is not the end of it all. And so even though there can be fear within us that soothing voice of God which tells us that we are going to be with him will comfort and soothe our fears.
I have seen many Christians who in their last days have barely shown any fear. My grandad told us in the morning of his death that he was going to die and asked us to sit around him and sing hymns. He refused to go to the hospital, he wanted to die in our presence. There was that peace that passeth all understanding which had a huge impact on me as a teenager. I did not see any fear in his eyes. The overwhelming peace of God which he had displayed throughout his life gave him a strong sense of hope that melted the fear away.