The well, Fairstar's first oil and gas well, will be drilled to a total depth of 1000m and is targeting oil and gas.
Hunt Energy's rig is expected to take about two weeks to drill the well to its planned total depth.
Fairstar has paid Knight $1 million for the cost of drilling the well to earn a 60% stake in PEP 165.
The company has previously said that existing regional seismic data has shown that Cooper Basin-equivalent sections may be present in the permit.