An individualised (HRTF) is very important for creating realistic (VR) and (AR) environments. However, acoustically measuring high-quality HRTFs requires expensive equipment and an acoustic lab setting. To overcome these limitations and to make this measurement more efficient HRTF upsampling has been exploited in the past where a high-resolution HRTF is created from a low-resolution one. This paper demonstrates how (GAN) can be applied to HRTF upsampling. We propose a novel approach that transforms the HRTF data for direct use with a convolutional (SRGAN). This new approach is benchmarked against three baselines: barycentric upsampling, (SH) upsampling and an HRTF selection approach. Experimental results show that the proposed method outperforms all three baselines in terms of (LSD) and localisation performance using perceptual models when the input HRTF is sparse (less than 20 measured positions).