In this paper, we investigate the application of Gabor Frames (GFs) as an effective Time-Frequency (TF) analysis tool for compressing digital holograms. Our choice of GFs stems from their notable flexibility and accuracy in TF decomposition. Unlike some other techniques, GFs offer the advantage of accommodating both overcomplete and orthonormal signal representations. Furthermore, GFs have a robust mathematical foundation, opening doors to a broad spectrum of potential applications beyond compression. First, we provide an overview of essential concepts in GFs theory like dual GFs, analysis and synthesis operators. Second, we illustrate how GFs can be employed for digital holograms representation in the phase space domain. For compression purpose, we substitute the Short-Time Fourier Transform (STFT) used in the JPEG-PLENO Holography codec by tight GFs, and compare their encoding performance. We present and thoroughly discuss the rate-distortion graphs, shedding light on the efficacy of GFs in digital hologram lossy compression.