This letter addresses the problem of beam pattern re-synthesis due to Transmit/Receive Module (TRM) malfunctions in active phased array antenna systems. Since TRM failures in full array systems cause beam pattern distortion and degrade system performance, a re-synthesis technique to compensate for these failures is essential. Conventional optimization algorithms, such as the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), suffer from high computational costs that hinder real-time application, while deep learning-based approaches are limited by the requirement for large-scale training datasets. To resolve these issues, this letter proposes a transfer learning-based beam pattern re-synthesis technique. The proposed method pre-trains the physical principles of beamforming using the array factor and derives compensation weights by fine-tuning with a small amount of optimization data. In addition, a compound loss function is designed to prevent gain degradation during the re-synthesis process. Simulation results demonstrate that the proposed technique achieves a 40% lower Mean Squared Error (MSE) compared to a model without pre-training using only 1,000 fine-tuning samples, while recovering the peak gain to 97.9% of the nominal level.