Individual Head-Related Transfer Functions (HRTFs) are starting to be introduced in many commercial immersive audio applications and are crucial for realistic spatial audio rendering. However, one of the main hesitations regarding their introduction is that creating individual HRTFs is impractical at scale due to the complexities of the HRTF measurement process. To mitigate this drawback, HRTF spatial upsampling has been proposed with the aim of reducing the measurements required. While prior work has seen success with different machine learning (ML) approaches, these models often struggle with long-range preservation of local spatial variation patterns across neighbouring source directions and generalization at high upsampling factors. In this paper, we propose a novel transformer-based architecture for HRTF upsampling, leveraging the attention mechanism to better capture spatial correlations across the HRTF sphere. Working in the spherical harmonic (SH) domain, our model learns to reconstruct high-resolution HRTFs from sparse input measurements with significantly improved accuracy. To enhance spatial coherence, we introduce a neighbour dissimilarity loss that promotes magnitude smoothness, yielding more realistic upsampling. We evaluate our method using both perceptual localization models and objective spectral distortion metrics. Experiments show that our model outperforms existing methods across several evaluation metrics in generating realistic, high-fidelity HRTFs.