Accurate segmentation of the optic disc and cup is critical for the early diagnosis and management of ocular diseases such as glaucoma. However, segmentation models trained on one dataset often suffer significant performance degradation when applied to target data acquired under different imaging protocols or conditions. To address this challenge, we propose \textbf{Grad-CL}, a novel source-free domain adaptation framework that leverages a pre-trained source model and unlabeled target data to robustly adapt segmentation performance without requiring access to the original source data. Grad-CL combines a gradient-guided pseudolabel refinement module with a cosine similarity-based contrastive learning strategy. In the first stage, salient class-specific features are extracted via a gradient-based mechanism, enabling more accurate uncertainty quantification and robust prototype estimation for refining noisy pseudolabels. In the second stage, a contrastive loss based on cosine similarity is employed to explicitly enforce inter-class separability between the gradient-informed features of the optic cup and disc. Extensive experiments on challenging cross-domain fundus imaging datasets demonstrate that Grad-CL outperforms state-of-the-art unsupervised and source-free domain adaptation methods, achieving superior segmentation accuracy and improved boundary delineation. Project and code are available at https://visdomlab.github.io/GCL/.