Organizations are reluctant to hire emotionally exhausted employees. However, current research has partially explored the implications of retaining both emotionally intelligent and emotionally exhausted employees. Hence, the question arises: do emotionally intelligent employees always remain meaningfully engaged in their work? And do emotionally exhausted employees adversely impact the organization? In our study, we empirically examined the role of ethical climate in assessing the impact of employees’ emotional intelligence and exhaustion on their work engagement. We collected data from 450 employees of private sector banks in India. The results showed that an ethical climate was positively correlated with employees’ work engagement. Additionally, we found that the influence of emotional intelligence was positive and emotional exhaustion was negative on employee engagement. Interestingly, in organizations with a strong ethical climate, emotionally intelligent employees did not display significantly higher engagement. However, emotionally exhausted employees appeared more engaged in such environments. These findings underscored the importance of re-evaluating the role of ethical climate and its influence on the work engagement of customer-contact employees with different emotional capacities.