Pronoun translation is a longstanding challenge in neural machine translation (NMT), often requiring inter-sentential context to ensure linguistic accuracy. To address this, we introduce ProNMT, a novel framework designed to enhance pronoun and overall translation quality in context-aware machine translation systems. ProNMT leverages Quality Estimation (QE) models and a unique Pronoun Generation Likelihood-Based Feedback mechanism to iteratively fine-tune pre-trained NMT models without relying on extensive human annotations. The framework combines QE scores with pronoun-specific rewards to guide training, ensuring improved handling of linguistic nuances. Extensive experiments demonstrate significant gains in pronoun translation accuracy and general translation quality across multiple metrics. ProNMT offers an efficient, scalable, and context-aware approach to improving NMT systems, particularly in translating context-dependent elements like pronouns.