This research addresses the critical challenge of implementing Digital Pre-Distortion (DPD) in Hybrid Beamformer (HBF) systems, focusing on the inherent trade-off between Power Amplifier (PA) efficiency and signal linearity. The study makes several key contributions, beginning with a novel Genetic Algorithm (GA) designed to optimise the combined response of the PA array, which yields an accurate DPD solution and significantly improves the Adjacent Channel Power Ratio (ACPR). A computationally efficient DPD method is also developed, utilising distinct pre-distorting coefficients for different signal segments and targeting the most distorted sub-samples to enhance ACPR with fewer coefficients. Furthermore, the research proposes three techniques to linearise the PA response and calibrate the RF system by leveraging signal characteristics, thereby addressing mismatches within the HBF. Finally, an adaptive Iterative Learning Control (ILC) DPD architecture is presented to rectify distortion in HBF. Overall, this thesis contributes a suite of efficient DPD techniques that mitigate PA distortion in HBFs, demonstrating the potential to improve signal quality and reduce the computational process.