Q - Is it a sin to fear death?
A - Thanks for the question. The simple answer is no. Fear is an emotional response to a situation. There is no sin in feeling a certain way. Even Jesus feared the suffering that he was to undergo and the death he was to have. We see this when he asks His Father to take the cup from him.
But, we should also follow Christ's example when he abandons himself to the Father's will. Fear can lead to sin, when we allow it to rule our lives. For example, if out of fear, we failed to act in a way that justice or love demanded of us, then we have sinned.
So, the feeling itself isn't sinful, but can lead to sin if we do what we ought not do or don't do what we ought. (For more - here is St. Thomas Aquinas take on fear and sin.)
On a slightly different note, while it is quite natural to have somewhat of a fear of the unknown, this is where we need to develop the virtue of hope. We should pray for God to increase hope in us and then do our best to hope in God's loving providence. He is in control and our hope must be anchored in the mystery of the Resurrection.
Through sin, death entered the world. Through Christ dying and rising again, He conquered death. We participate in this act of salvation through believing in Christ's grace for us and that we will one day be with Him forever in heaven.
May the hope of Christ bring us beyond our fears!
"'Blessed are the dead who die in the Lord henceforth'. "Blessed indeed', says the Spirit, "that they may rest from their labours, for their deeds follow them!'" (Rv 14:13).