Jonathan Creswell, 36, who has an address which cannot be disclosed due to a reporting restrictionr, has denied the murdering Ms Simpson following an incident in Gortnessy Meadows, Lettershandoney, on August 3, 2020.
Ms Simpson, who was originally from the village of Tynan in Co Armagh but had been living in Donegal, died in Altnagelvin Hospital six days later, having never regained consciousness.
The defendant, who is currently on bail, is also accused of raping Ms Simpson on a date unknown between 2 August 2020 and 4 August 2020.
The jury was selected at Derry Crown Court, sitting in Coleraine, on Monday where the prosecution will open the case on Tuesday.
Three women have already pleaded guilty to charges in connection with the death of the young showjumper.
The trial is expected to last up to six weeks and is being presided over by the Recorder of Derry, Judge Neil Rafferty KC.