The use of an external microphone in conjunction with an existing local microphone array can be particularly beneficial for noise reduction tasks that are critical for hearing devices, such as cochlear implants and hearing aids. Recent work has already demonstrated how an external microphone signal can be effectively incorporated into the common noise reduction technique of using a Minimum Variance Distortionless Response (MVDR) beamformer. In this paper, we provide a further extension, whereby an external microphone signal can be incorporated into an existing framework of a Generalised Sidelobe Canceller (GSC) that has been designed for a local microphone signal array. It will be shown that the resulting GSC with an external microphone results in an easily implementable addition to the existing GSC framework for a local microphone array, and can exhibit an improved noise reduction performance.