The presence of a priest during the funeral is not necessary even if preferable.
Without generalising, we must admit that funerals are held more and more often without a priest. And we can easily imagine that this will be more and more frequent in the coming years.
This is explained by the lack of priests and the increasing charge of work they have to accomplish. It is therefore not possible for them to ensure all funeral services.
In most parishes, laymen are trained and teams are constituted in order to follow families through sorrow, listen to them and prepare the ceremony together with them.
Some families could be surprised, even disappointed, when funerals are celebrated without a priest. They deeply desire, for a member of their family, that it should be a priest. But after this first reaction, they discover the funeral teams, fellow Christians, ready to welcome them and to follow them, and they become grateful.
Even more, the priest can celebrate a Mass for the deceased during a Sunday following the funeral.